Project-team positioning

Evaluating the scalability, robustness, energy consumption and performance of large infrastructures such as exascale platforms and clouds raises severe methodological challenges. The complexity of such platforms mandates empirical evaluation but direct experimentation via an application deployment on a real-world testbed is often limited by the few platforms available at hand and is even sometimes impossible (cost, access, early stages of the infrastructure design, etc.). Furthermore, such experiments are costly, difficult to control and therefore difficult to reproduce. Although many of these digital systems have been built by human, they have reached such a complexity level that we are no longer able to study them like artificial systems and have to deal with the same kind of experimental issues as natural sciences. The development of a sound experimental methodology for the evaluation of resource management solutions is among the most important ways to cope with the growing complexity of computing environments. Although computing environments come with their own specific challenges, we believe such general observation problems should be addressed by borrowing good practices and techniques developed in many other domains of science, in particular (1) Predictive Simulation, (2) Trace Analysis and Visualization, and (3) the Design of Experiments.

Scientific achievements

Large computing systems are particularly complex to understand because of the interplay between their discrete nature (originating from deterministic computer programs) and their stochastic nature (emerging from the physical world, long distance interactions, and complex hardware and software stacks). A first line of research in POLARIS is devoted to the design of relatively simple statistical models of key components of distributed systems and their exploitation to feed simulators of such systems, to build aggregated performance views, and to detect anomalous behaviors.

Project-team positioning

Stochastic models often suffer from the curse of dimensionality: their complexity grows exponentially with the number of dimensions of the system. At the same time, very large stochastic systems are sometimes easier to analyze: it can be shown that some classes of stochastic systems simplify as their dimension goes to infinity because of averaging effects such as the law of large numbers, or the central limit theorem. This forms the basis of what is called an asymptotic method, which consists in studying what happens when a system gets large in order to build an approximation that is easier to study or to simulate.

Within the team, the research that we conduct in this axis is to foster the applicability of these asymptotic methods to new application areas. This leads us to work on the application of classical methods to new problems, but also to develop new approximation methods that take into account special features of the systems we study (i.e., moderate number of dimensions, transient behavior, random matrices). Typical applications are mean field method for performance evaluation, application to distributed optimization, and more recently statistical learning. One originality of our work is to quantify precisely what is the error made by such approximations. This allows us to define refinement terms that lead to more accurate approximations.

Scientific achievements

Project-team positioning

Online learning concerns the study of repeated decision-making in changing environments. Of course, depending on the context, the words “learning” and “decision-making” may refer to very different things: in economics, this could mean predicting how rational agents react to market drifts; in data networks, it could mean adapting the way packets are routed based on changing traffic conditions; in machine learning and AI applications, it could mean training a neural network or the guidance system of a self-driving car; etc. In particular, the changes in the learner's environment could be either exogenous (that is, independent of the learner's decisions, such as the weather affecting the time of travel), or endogenous (i.e., they could depend on the learner's decisions, as in a game of poker), or any combination thereof. However, the goal for the learner(s) is always the same: to make more informed decisions that lead to better rewards over time.

The study of online learning models and algorithms dates back to the seminal work of Robbins, Nash and Bellman in the 50's, and it has since given rise to a vigorous research field at the interface of game theory, control and optimization, with numerous applications in operations research, machine learning, and data science. In this general context, our team focuses on the asymptotic behavior of online learning and optimization algorithms, both single- and multi-agent: whether they converge, at what speed, and/or what type of non-stationary, off-equilibrium behaviors may arise when they do not.

The focus of POLARIS on game-theoretic and Markovian models of learning covers a set of specific challenges that dovetail in a highly synergistic manner with the work of other learning-oriented teams within Inria (like SCOOL in Lille, SIERRA in Paris, and THOTH in Grenoble), and it is an important component of Inria's activities and contributions in the field (which includes major industrial stakeholders like Google / DeepMind, Facebook, Microsoft, Amazon, and many others).

Scientific achievements

Our team's work on online learning covers both single- and multi-agent models; in the sequel, we present some highlights of our work structured along these basic axes.

In the single-agent setting, an important problem in the theory of Markov decision processes – i.e., discrete-time control processes with decision-dependent randomness – is the so-called “restless bandit” problem. Here, the learner chooses an action – or “arm” – from a finite set, and the mechanism determining the action's reward changes depending on whether the action was chosen or not (in contrast to standard Markov problems where the activation of an arm does not have this effect). In this general setting, Whittle conjectured – and Weber and Weiss proved – that Whittle's eponymous index policy is asymptotically optimal. However, the result of Weber and Weiss is purely asymptotic, and the rate of this convergence remained elusive for several decades. This gap was finally settled in a series of POLARIS papers 6970, where we showed that Whittle indices (as well as other index policies) become optimal at a geometric rate under the same technical conditions used by Weber and Weiss to prove Whittle's conjecture, plus a technical requirement on the non-singularity of the fixed point of the mean-field dynamics. We also propose the first sub-cubic algorithm to compute Whittle and Gittins indexes. As for reinforcement learning in Markovian bandits, we have shown that Bayesian and optimistic approaches do not use the structure of Markovian bandits similarly: While Bayesian learning has both a regret and a computational complexity that scales linearly with the number of arms, optimistic approaches all incur an exponential computation time, at least in their current versions 68.

In the multi-agent setting, our work has focused on the following fundamental question:

Does the concurrent use of (possibly optimal) single-agent learning algorithms

ensure convergence to Nash equilibrium in multi-agent, game-theoretic environments?

Conventional wisdom might suggest a positive answer to this question because of the following “folk theorem”: under no-regret learning, the agents' empirical frequency of play converges to the game's set of coarse correlated equilibria. However, the actual implications of this result are quite weak: First, it concerns the empirical frequency of play and not the day-to-day sequence of actions employed by the players. Second, it concerns coarse correlated equilibria which may be supported on strictly dominated strategies – and are thus unacceptable in terms of rationalizability. These realizations prompted us to make a clean break with conventional wisdom on this topic, ultimately showing that the answer to the above question is, in general, “no”: specifically, 96, 94 showed that the (optimal) class of “follow-the-regularized-leader” (FTRL) learning algorithms leads to Poincaré recurrence even in simple, $2\times 2$ min-max games, thus precluding convergence to Nash equilibrium in this context.

This negative result generated significant interest in the literature as it contributed in shifting the focus towards identifying which Nash equilibria may arise as stable limit points of FTRL algorithms and dynamics. Earlier work by POLARIS on the topic 52, 97, 98 suggested that strict Nash equilibria play an important role in this question. This suspicion was recently confirmed in a series of papers 64, 81 where we established a sweeping negative result to the effect that mixed Nash equilibria are incompatible with no-regret learning. Specifically, we showed that any Nash equilibrium which is not strict cannot be stable and attracting under the dynamics of FTRL, especially in the presence of randomness and uncertainty. This result has significant implications for predicting the outcome of a multi-agent learning process because, combined with 97, it establishes the following far-reaching equivalence: a state is asymptotically stable under no-regret learning if and only if it is a strict Nash equilibrium.

Going beyond finite games, this further raised the question of what type of non-convergent behaviors can be observed in continuous games – such as the class of stochastic min-max problems that are typically associated to generative adversarial networks (GANs) in machine learning. This question was one of our primary collaboration axes with EPFL, and led to a joint research project focused on the characterization of the convergence properties of zeroth-, first-, and (scalable) second-order methods in non-convex/non-concave problems. In particular, we showed in 85 that these state-of-the-art min-max optimization algorithms may converge with arbitrarily high probability to attractors that are in no way min-max optimal or even stationary – and, in fact, may not even contain a single stationary point (let alone a Nash equilibrium). Spurious convergence phenomena of this type can arise even in two-dimensional problems, a fact which corroborates the empirical evidence surrounding the formidable difficulty of training GANs.

Project-team positioning

The topics in this axis emerge from current social and economic questions rather than from a fixed set of mathematical methods. To this end we have identified large trends such as energy efficiency, fairness, privacy, and the growing number of new market places. In addition, COVID has posed new questions that opened new paths of research with strong links to policy making.

Throughout these works, the focus of the team is on modeling aspects of the aforementioned problems, and obtaining strong theoretical results that can give high-level guidelines on the design of markets or of decision-making procedures. Where relevant, we complement those works by measurement studies and audits of existing systems that allow identifying key issues. As this work is driven by topics, rather than methods, it allows for a wide range of collaborations, including with enterprises (e.g., Naverlabs), policy makers, and academics from various fields (economics, policy, epidemiology, etc.).

Other teams at Inria cover some of the societal challenges listed here (e.g., PRIVATICS, COMETE) but rather in isolation. The specificity of POLARIS resides in the breadth of societal topics covered and of the collaborations with non-CS researchers and non-research bodies; as well as in the application of methods such as game theory to those topics.

Scientific achievements

7.1.1 SimGrid

• Keywords:
  Large-scale Emulators, Grid Computing, Distributed Applications
• Scientific Description:

  SimGrid is a toolkit that provides core functionalities for the simulation of distributed applications in heterogeneous distributed environments. The simulation engine uses algorithmic and implementation techniques toward the fast simulation of large systems on a single machine. The models are theoretically grounded and experimentally validated. The results are reproducible, enabling better scientific practices.

  Its models of networks, cpus and disks are adapted to (Data)Grids, P2P, Clouds, Clusters and HPC, allowing multi-domain studies. It can be used either to simulate algorithms and prototypes of applications, or to emulate real MPI applications through the virtualization of their communication, or to formally assess algorithms and applications that can run in the framework.

  The formal verification module explores all possible message interleavings in the application, searching for states violating the provided properties. We recently added the ability to assess liveness properties over arbitrary and legacy codes, thanks to a system-level introspection tool that provides a finely detailed view of the running application to the model checker. This can for example be leveraged to verify both safety or liveness properties, on arbitrary MPI code written in C/C++/Fortran.

• Functional Description:
  SimGrid is a simulation toolkit that provides core functionalities for the simulation of distributed applications in large scale heterogeneous distributed environments.
• Release Contributions:

  The Anne of Brittany release (she became a Duchess 536 years ago).

  * Various improvements and unification of the simulation APIs * MC: Enable the verification of Python programs, and of condvars and iprobe calls. * MC: Exhibit the critical transition when a failure is found. * (+ internal refactoring and bug fixes)

• News of the Year:

  There were 2 major releases in 2023. On modeling aspects, we released new plugins simulating chiller, photovoltaic and battery components of Fog/Edge infrastructures, as well as the disk arrays used in desegregated infrastructures. We improved the consistency of the simulation core: the new ActivitySet containers now make it easy to way for the completion of an heterogeneous set of activities (computation, communication, I/O, etc). The simulation of workflow and dataflow applications was also streamlined, with more examples, more documentation and less bugs. A new model of activities mixing disk I/O and network communication was introduced, to efficiently simulate accesses to remote disks. In addition, many efforts were put on the profiling of the software, leading to massive performance gains. We also pursued our efforts to improve the overall framework, through bug fixes, code refactoring and other software quality improvements. In particular, interfaces that were deprecated since almost a decade were removed to ease the maintenance burden on our community.

  Many improvement occurred on the model-checker side too. We dropped the old experiments toward stateful verification of liveness properties to boost the development of stateless verification of safety properties. Our tool is simpler internally, and usable on all major operating systems. We modernized the reduction algorithms, implementing several recent algorithms of the literature and paving the way to the introduction of new ones. We also introduced a new module allowing to verify not only distributed applications, but also threaded applications.

• URL:
  https://­simgrid.­org/
• Contact:
  Martin Quinson
• Participants:
  Adrien Lebre, Anne-Cécile Orgerie, Arnaud Legrand, Augustin Degomme, Arnaud Giersch, Emmanuelle Saillard, Frédéric Suter, Jonathan Pastor, Martin Quinson, Samuel Thibault
• Partners:
  CNRS, ENS Rennes

7.1.2 PSI

• Name:
  Perfect Simulator
• Keywords:
  Markov model, Simulation
• Functional Description:
  Perfect simulator is a simulation software of markovian models. It is able to simulate discrete and continuous time models to provide a perfect sampling of the stationary distribution or directly a sampling a functional of this distribution by using coupling from the past. The simulation kernel is based on the CFTP algorithm, and the internal simulation of transitions on the Aliasing method.
• URL:
  https://­gitlab.­inria.­fr/­PSI/­psi3/
• Contact:
  Jean-Marc Vincent

7.1.3 marmoteCore

• Name:
  Markov Modeling Tools and Environments - the Core
• Keywords:
  Modeling, Stochastic models, Markov model
• Functional Description:

  marmoteCore is a C++ environment for modeling with Markov chains. It consists in a reduced set of high-level abstractions for constructing state spaces, transition structures and Markov chains (discrete-time and continuous-time). It provides the ability of constructing hierarchies of Markov models, from the most general to the particular, and equip each level with specifically optimized solution methods.

  This software was started within the ANR MARMOTE project: ANR-12-MONU-00019.

• URL:
  https://­gitlab.­inria.­fr/­PSI/­marmotecore/
• Publications:
  hal-01651940, hal-01276456
• Contact:
  Alain Jean-Marie
• Participants:
  Alain Jean-Marie, Hlib Mykhailenko, Benjamin Briot, Franck Quessette, Issam Rabhi, Jean-Marc Vincent, Jean-Michel Fourneau
• Partners:
  Université de Versailles St-Quentin-en-Yvelines, Université Paris Nanterre

7.1.4 MarTO

• Name:
  Markov Toolkit for Markov models simulation: perfect sampling and Monte Carlo simulation
• Keywords:
  Perfect sampling, Markov model
• Functional Description:
  MarTO is a simulation software of markovian models. It is able to simulate discrete and continuous time models to provide a perfect sampling of the stationary distribution or directly a sampling of functional of this distribution by using coupling from the past. The simulation kernel is based on the CFTP algorithm, and the internal simulation of transitions on the Aliasing method. This software is a rewrite, more efficient and flexible, of PSI
• URL:
  https://­gitlab.­inria.­fr/­MarTo/­marto
• Contact:
  Vincent Danjean

7.1.5 GameSeer

• Keyword:
  Game theory
• Functional Description:
  GameSeer is a tool for students and researchers in game theory that uses Mathematica to generate phase portraits for normal form games under a variety of (user-customizable) evolutionary dynamics. The whole point behind GameSeer is to provide a dynamic graphical interface that allows the user to employ Mathematica's vast numerical capabilities from a simple and intuitive front-end. So, even if you've never used Mathematica before, you should be able to generate fully editable and customizable portraits quickly and painlessly.
• URL:
  http://­polaris.­imag.­fr/­panayotis.­mertikopoulos/­publications/­s01-gameseer/
• Contact:
  Panayotis Mertikopoulos

7.1.6 rmf_tool

• Name:
  A library to Compute (Refined) Mean Field Approximations
• Keyword:
  Mean Field
• Functional Description:

  The tool accepts three model types:

  - homogeneous population processes (HomPP)

  - density dependent population processes (DDPPs)

  - heterogeneous population models (HetPP)

  In particular, it provides a numerical algorithm to compute the constant of the refined mean field approximation provided in the paper "A Refined Mean Field Approximation" by N. Gast and B. Van Houdt, SIGMETRICS 2018, and a framework to compute heterogeneous mean field approximations as proposed in "Mean Field and Refined Mean Field Approximations for Heterogeneous Systems: It Works!" by N. Gast and S. Allmeier, SIGMETRICS 2022.

• URL:
  https://­github.­com/­ngast/­rmf_tool
• Publications:
  hal-01622054, tel-02509756, hal-03485044
• Contact:
  Nicolas Gast

7.1.7 SCIP

• Name:
  Solving Constraint Integer Programs
• Keywords:
  Linear optimization, Mathematical Optimization, Mixed Integer Programming
• Functional Description:
  SCIP is currently one of the fastest non-commercial solvers for mixed integer programming (MIP) and mixed integer nonlinear programming (MINLP). It is also a framework for constraint integer programming and branch-cut-and-price. It allows for total control of the solution process and the access of detailed information down to the guts of the solver.
• Release Contributions:

  SCIP 9.2.0 Features

  added check for absolute and relative gap limits at end of synchronization in concurrent solving mode, in order to terminate earlier, note that if the concurrent solve is stopped due to a gap limit, the "winner" solver will have an interrupted solution status and its primal and dual bounds may not be the best possible ones (use SCIPgetConcurrentPrimalbound() and SCIPgetConcurrentDualbound() instead) parse pseudoboolean constraint from CIP format (and add linear-"and"-reformulation)

  Performance improvements

  reoptimization now also stores propagations from propagators if reoptimization/saveconsprop is enabled, the parameter will be renamed to reoptimization/saveprop in a next major release imposed stricter limits on the size of disconnected components which may be solved separately during presolve use individual slack variables also for constraints indicated by a common binary variable to use tighter formulation by default when computing symmetries using Nauty, iteration limits are now available to terminate Nauty early

  Fixed bugs

  Benders' decomposition subproblems that are always infeasible are correctly handled and the complete problem is declared infeasible skip linear constraint propagation if the residual activity bound cancels the side precision correct bound tracking to make the evaluation of primal-dual-integrals work skip aggregations on fixed variables in milp presolver to avoid errors for earlier versions of PaPILO use indices of negation counterparts and accept fixings when ordering and-resultants of pseudoboolean constraints update locks on model variables before removing pseudoboolean constraints in presolve reformulate soft pseudoboolean constraints with linear constraints if the indicator decomposition is disabled add workaround for recent HiGHS versions resetting the model status when changing the presolve option after a solve avoid hashmap key error in removal of doubletons and singletons in dual presolve of setppc constraints by updating constraints and corresponding hashmaps after each multi-aggregation

  Interface changes New API functions

  added SCIPtpiIsAvailable() to check whether a working task processing interface is available (TPI != none) added SCIPtpiGetLibraryName() and SCIPtpiGetLibraryDesc() SCIPdelCons() can now also be called in SCIP_STAGE_TRANSFORMED added SCIPstrcasecmp() and SCIPstrncasecmp() for case-insensitive string comparison added SCIPbendersSubproblemsAreInfeasible() to return if at least one subproblem has been identified as being infeasible prior to performing any variable fixing

  New parameters

  presolving/milp/abortfacexhaustive to control the abort threshold for exhaustive presolving in PAPILO presolving/milp/abortfacmedium to control the abort threshold for medium presolving in PAPILO presolving/milp/abortfacfast to control the abort threshold for fast presolving in PAPILO constraints/components/maxcompweight to determine the maximum weight for a disconnected component that is solved during presolve constraints/components/contfactor counts the contributing factor of a single continuous variables with respect to the weight limit specified by constraints/components/maxcompweight constraints/indicator/usesameslackvar to decide whether the same slack variable should be used for indicators constraints with common binary variable propagating/symmetry/nautymaxncells and propagating/symmetry/nautymaxnnodes to set iteration limits in Nauty (only available if build with SYM=nauty or SYM=snauty)

  Changed parameters

  presolving/milp/threads is now only available if PaPILO is built with TBB changed default of numerics/recomputefac to 1e+6 to aim at relative epsilon precision

  Build system Cmake

  attempted to fix detection of CPLEX library on macOS and Windows systems

  Testing

  added parameter FILTER for tests/Makefile to run only tests with a specific pattern (ctest with -R FILTER)

  Miscellaneous

  adjusted Gurobi interface for Gurobi 12 reordered events: BESTSOLFOUND/NODE_FEASIBLE are now processed before the nodes are cut off and before NODE_DELETE events are processed removed #define of getcwd (in case of Windows builds) in scip/def.h the #define of strcasecmp and strncasecmp (in case of Windows builds) in scip/def.h will be removed with SCIP 10, use SCIPstr(n)casecmp() (scip/pub_misc.h) instead

• URL:
  https://­www.­scipopt.­org/
• Contact:
  Mathieu Besancon
• Partners:
  TU Darmstadt, RWTH Aachen University, Friedrich-Alexander-Universität Erlangen-Nürnberg, Eindhoven University of Technology, University of Twente, University of Bayreuth, Forschungscampus Modal

Dispatching and scheduling multiserver jobs for throughput optimality

In 1, we consider the problem of dispatching and scheduling an infinite stream of multiple classes of jobs to a set of single server parallel queues. Each job requires the simultaneous utilization of multiple servers. Our objective is to identify a dispatching algorithm (used by a central dispatcher) and a scheduling discipline (used by each server) that induces throughput optimality, i.e., the mean response time of jobs is finite whenever the system load is less than one. It is known that this problem is not trivial even in the case where all servers share a centralized queue, i.e., no job dispatching. We show that throughput optimality can be obtained by dispatching jobs to queues according to probabilities provided that i) jobs of a given class respect some constraint on the server geometry and ii) the scheduling discipline prioritizes jobs with the largest server need. Due to a connection with the $M/G/1$ priority queue, we provide an exact analytical expression for the mean response time of jobs. Finally, we discuss the connection of our model with redundancy systems, where jobs do not necessarily require the simultaneous utilization of servers.

Load Balancing with Job-Size Testing: Performance Improvement or Degradation?

In the context of decision making under explorable uncertainty, scheduling with testing is a powerful technique used in the management of computer systems to improve performance via better job-dispatching decisions. Upon job arrival, a scheduler may run some testing algorithm against the job to extract some information about its structure, e.g., its size, and properly classify it. The acquisition of such knowledge comes with a cost because the testing algorithm delays the dispatching decisions, though this is under control. In 4, we analyze the impact of such extra cost in a load balancing setting by investigating the following questions: does it really pay off to test jobs? If so, under which conditions? Under mild assumptions connecting the information extracted by the testing algorithm in relationship with its running time, we show that whether scheduling with testing brings a performance degradation or improvement strongly depends on the traffic conditions, system size and the coefficient of variation of job sizes. Thus, the general answer to the above questions is non-trivial and some care should be considered when deploying a testing policy. Our results are achieved by proposing a load balancing model for scheduling with testing that we analyze in two limiting regimes. When the number of servers grows to infinity in proportion to the network demand, we show that job-size testing actually degrades performance unless short jobs can be predicted reliably almost instantaneously and the network load is sufficiently high. When the coefficient of variation of job sizes grows to infinity, we construct testing policies inducing an arbitrarily large performance gain with respect to running jobs untested.

Balanced Splitting: A Framework for Achieving Zero-wait in the Multiserver-job Model

In 3, we present a new framework for designing nonpreemptive and job-size oblivious scheduling policies in the multiserver-job queueing model. The main requirement is to identify a static and balanced sub-partition of the server set and ensure that the servers in each set of that sub-partition can only handle jobs of a given class and in a first-come first-served order. A job class is determined by the number of servers to which it has exclusive access during its entire execution and the probability distribution of its service time. This approach aims to reduce delays by preventing small jobs from being blocked by larger ones that arrived first, and it is particularly beneficial when the job size variability intra resp. inter classes is small resp. large. In this setting, we propose a new scheduling policy, Balanced-Splitting. In our main results, we provide a sufficient condition for the stability of Balanced-Splitting and show that the resulting queueing probability, i.e., the probability that an arriving job needs to wait for processing upon arrival, vanishes in both the subcritical (the load is kept fixed to a constant less than one) and critical (the load approaches one from below) many-server limiting regimes. Crucial to our analysis is a connection with the $M/GI/s/s$ queue and Erlang's loss formula, which allows our analysis to rely on fundamental results from queueing theory. Numerical simulations show that the proposed policy performs better than several preemptive/nonpreemptive size-aware/oblivious policies in various practical scenarios. This is also confirmed by simulations running on real traces from High Performance Computing (HPC) workloads. The delays induced by Balanced-Splitting are also competitive with those induced by state-of-the-art policies such as First-Fit-SRPT and ServerFilling-SRPT, though our approach has the advantage of not requiring preemption, nor the knowledge of job sizes.

Asynchronous Load Balancing and Auto-scaling: Mean-Field Limit and Optimal Design

In 2, we develop a Markovian framework for load balancing that combines classical algorithms such as Power-of-$d$ with auto-scaling mechanisms that allow the net service capacity to scale up or down in response to the current load on the same timescale as job dynamics. Our framework is inspired by serverless platforms, such as Knative, where servers are software functions that can be flexibly instantiated in milliseconds according to scaling rules defined by the users of the serverless platform. The main question is how to design such scaling rules to minimize user-perceived delay performance while ensuring low energy consumption. For the first time, we investigate this problem when the auto-scaling and load balancing processes operate asynchronously (or proactively), as in Knative. In contrast to the synchronous (or reactive) paradigm, asynchronism brings the advantage that jobs do not necessarily need to wait any time a scale-up decision is taken. In our main result, we find a general condition on the structure of scaling rules able to drive mean-field dynamics to delay and relative energy optimality, i.e., a situation where both the user-perceived delay and the relative energy waste induced by idle servers vanish in the limit where the network demand grows to infinity in proportion to the nominal service capacity. The identified condition suggests to scale up the current net capacity if and only if the mean demand exceeds the rate at which servers become idle and active. Finally, we propose a family of scaling rules that satisfy our optimality condition. Numerical simulations demonstrate that these rules provide better delay performance than existing synchronous auto-scaling schemes while inducing almost the same power consumption.

A Stochastic Approach for Scheduling AI Training Jobs in GPU-based Systems

In 10, we optimize the scheduling of Deep Learning (DL) training jobs from the perspective of a Cloud Service Provider running a data center, which efficiently selects resources for the execution of each job to minimize the average energy consumption while satisfying time constraints. To model the problem, we first develop a Mixed-Integer Non-Linear Programming formulation. Unfortunately, the computation of an optimal solution is prohibitively expensive, and to overcome this difficulty, we design a heuristic STochastic Scheduler (STS). Exploiting the probability distribution of early termination, STS determines how to adapt the resource assignment during the execution of the jobs to minimize the expected energy cost while meeting the job due dates. The results of an extensive experimental evaluation show that STS guarantees significantly better results than other methods in the literature, effectively avoiding due date violations and yielding a percentage total cost reduction between 32% and 80% on average. We also prove the applicability of our method in real-world scenarios, as obtaining optimal schedules for systems of up to 100 nodes and 400 concurrent jobs requires less than 5 seconds. Finally, we evaluated the effectiveness of GPU sharing, i.e., running multiple jobs in a single GPU. The obtained results demonstrate that depending on the workload and GPU memory, this further reduces the energy cost by 17-29% on average.

Mean Field Methods for Heterogeneous and Coupled Systems

Mean Field methods have consistently been of interest to the scientific community due to their capacity to approximate a wide range of stochastic population systems. This methodology has proven to be a cornerstone in understanding and predicting the behavior of large-scale, complex systems. The key idea of the mean field approximation is to replace the complex stochastic behavior of systems with a simpler deterministic counterpart. The approximation therefore assumes that individuals become increasingly independent for large system sizes. The behavior of the system is thus obtained by replacing individual interactions with the average state of individuals. Despite its longstanding application and the advancements made in various fields, numerous questions and challenges remain open. In the scope of the PhD thesis of Sebastian Allmeier 29, we present our contributions and advancements for two general types of population models (1) heterogeneous mean field models and (2) mean field models with fast-changing environment. In the first part of the thesis, we focus on stochastic systems with heterogeneous components. We consider two types of heterogeneity, individual-level diversity as well as graph-structured interactions. For both cases, we provide accuracy bounds for the expected state of finite-sized systems. The results are supported through practical examples, including cache replacement policies, supermarket models, load balancing, and bike-sharing systems, highlighting their computational tractability and precision. In the case of individual-level diversity, we further adapt the refined mean field idea and show that the refined approximation significantly reduces the error and provides accurate predictions for small to moderate-sized systems.In the second part of the thesis, we turn our focus to mean field approximation techniques for stochastic systems with a coupled, fast-changing environment. By studying the `average' mean field approximation, we obtain accuracy bounds for the expected system state. Furthermore, we derive a bias refinement term, which increases the accuracy of the approximation. Expanding on these results, we extend the methodology to stochastic approximation with constant step size and state-dependent Markovian noise. We show how to adapt the ideas to obtain accuracy results and a computable bias extension.

Computing the Bias of Constant-step Stochastic Approximation with Markovian Noise

This work has been published in several conferences, including 19, where we study stochastic approximation algorithms with Markovian noise and constant step-size $\alpha$. We develop a method based on infinitesimal generator comparisons to study the bias of the algorithm, which is the expected difference between ${\theta }_n$ — the value at iteration $n$ — and ${\theta }^{*}$ — the unique equilibrium of the corresponding ODE. We show that, under some smoothness conditions, this bias is of order $O\left(\alpha \right)$. Furthermore, we show that the time-averaged bias is equal to $\alpha V+O\left({\alpha }^2\right)$, where $V$ is a constant characterized by a Lyapunov equation, showing that $\mathrm{E}\left[{\overline{\theta }}_n\right]\approx {\theta }^{*}+V\alpha +O\left({\alpha }^2\right)$, where ${\overline{\theta }}_n=(1/n){\sum }_{k=1}^n{\theta }_k$ is the Polyak-Ruppert average. We also show that ${\overline{\theta }}_n$ converges with high probability around ${\theta }^{*}+\alpha V$. We illustrate how to combine this with Richardson-Romberg extrapolation to derive an iterative scheme with a bias of order $O\left({\alpha }^2\right)$.

Approximations to Study the Impact of the Service Discipline in Systems with Redundancy

Last, we have applied this technique to the study of queuing systems and difficult-to-study scheduling policies in cloud infrastructures, for example in 11. As job redundancy has been recognized as an effective means to improve performance of large-scale computer systems, queueing systems with redundancy have been studied by various authors. Existing results include methods to compute the queue length distribution and response time but only when the service discipline is First-Come-First-Served (FCFS). For other service disciplines, such as Processor Sharing (PS), or Last-Come-First-Served (LCFS), only the stability conditions are known. In this paper we develop the first methods to approximate the queue length distribution in a queueing system with redundancy under various service disciplines. We focus on a system with exponential job sizes, i.i.d. copies, and a large number of servers. We first derive a mean field approximation that is independent of the scheduling policy. In order to study the impact of service discipline, we then derive refinements of this approximation to specific scheduling policies. In the case of Processor Sharing, we provide a pair and a triplet approximation. The pair approximation can be regarded as a refinement of the classic mean field approximation and takes the service discipline into account, while the triplet approximation further refines the pair approximation. We also develop a pair approximation for three other service disciplines: First-Come-First-Served, Limited Processor Sharing and Last-Come-First-Served. We present numerical evidence that shows that all the approximations presented in the paper are highly accurate, but that none of them are asymptotically exact (as the number of servers goes to infinity). This makes these approximations suitable to study the impact of the service discipline on the queue length distribution. Our results show that FCFS yields the shortest queue length, and that the differences are more substantial at higher loads.

An MDP-Based Solution for the Energy Minimization of Non-Clairvoyant Hard Real-Time Systems

In 12, we address the problem of scheduling a possibly infinite sequence of hard real-time jobs on a single-core processor, with the dual goal that (1) all the jobs must finish before their deadline, and (2) the energy consumption must be minimized. The decision variable is the speed of the processor at each time instant, to be chosen from a finite set of available speeds. Our goal is to design a speed policy in charge of deciding, at each time instant, the speed of the processor in function of the job characteristics. We focus more specifically on the non-clairvoyant case, meaning that the actual size of the jobs (the amount of work to be done to complete the job) is unknown when they are released, but its probability distribution is known, and of course, the maximal size is known too. In this context, we propose two new speed policies, the optimal solution of a Markov Decision Process (called MOSP), and a heuristic speed policy called Expected Load (EL), obtained by adapting the classical policy Optimal Available (OA) to jobs with random sizes. Our MOSP algorithm is split in two phases: the first phase is offline — it computes the optimal processor speed for each possible system state — while the second phase is online — it retrieves the speed to apply to the processor thanks to a table lookup. Compared with the existing speed policies from the literature, MOSP achieves the optimal energy consumption but at the cost of a significant state space size. In contrast, EL achieves an energy consumption that is, on average, close to the optimal one obtained with MOSP, but at almost no cost in terms of state space.

Learning Optimal Admission Control in Partially Observable Queueing Networks

In 5, we present an efficient reinforcement learning algorithm that learns the optimal admission control policy in a partially observable queueing network. Specifically, only the arrival and departure times from the network are observable, and optimality refers to the average holding/rejection cost in infinite horizon. While reinforcement learning in Partially Observable Markov Decision Processes (POMDP) is prohibitively expensive in general, we show that our algorithm has a regret that only depends sub-linearly on the maximal number of jobs in the network, $S$. In particular, in contrast with existing regret analyses, our regret bound does not depend on the diameter of the underlying Markov Decision Process (MDP), which in most queueing systems is at least exponential in $S$. The novelty of our approach is to leverage Norton's equivalent theorem for closed product-form queueing networks and an efficient reinforcement learning algorithm for MDPs with the structure of birth-and-death processes.

Reoptimization Nearly Solves Weakly Coupled Markov Decision Processes

In 38, we propose a new policy, called the LP-update policy, to solve finite horizon weakly-coupled Markov decision processes. The latter can be seen as multi-constraint multi-action bandits, and generalize the classical restless bandit problems. Our solution is based on re-solving periodically a relaxed version of the original problem, that can be cast as a linear program (LP). When the problem is made of $N$ statistically identical sub-components, we show that the LP-update policy becomes asymptotically optimal at rate $O(T^2/\sqrt{N})$. This rate can be improved to $O(T/\sqrt{N})$ if the problem satisfies some ergodicity property and to $O(1/N)$ if the problem is non-degenerate. The definition of non-degeneracy extends the same notion for restless bandits. By using this property, we also improve the computational efficiency of the LP-update policy. We illustrate the performance of our policy on randomly generated examples, as well as a generalized applicant screening problem, and show that it outperforms existing heuristics.

Optimal Regrets in Markov Decision Processes

Last although regret is a common objective in Reinforcement Learning, other criteria are relevant and allow to better understand or discriminate algorithms. The thesis of Victor Boone 30, is dedicated to the theory of learning of Markov decision processes for the average reward criterion under the regret benchmark. Two standard formulations of the learning problem are investigated: the minimax and the model dependent settings. For both, asymptotic lower bounds of the regret are provided together with algorithms reaching them. Beyond the regret benchmark, the local behavior of classical algorithms is further studied and new learning metrics are designed for that matter.

8.4.1 Mixed Integer Optimization

8.4.2 Application to various domains

8.4.3 Optimization for Machine Learning

Many learning algorithms operate in centralized way, which raises many practical issues in terms of scalability, privacy, hence a high interest for designing efficient distributed and federated machine learning algorithms. Furthermore generally, the optimization space is also quite particular, which calls for specific regularization techniques and optimization algorithms.

A unified stochastic approximation framework for learning in games

In 14, we develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms, including gradient-based methods, the exponential / multiplicative weights algorithm for learning in finite games, optimistic and bandit variants of the above, etc. In addition to providing an integrated view of these algorithms, our framework further allows us to obtain several new convergence results, both asymptotic and in finite time, in both continuous and finite games. Specifically, we provide a range of criteria for identifying classes of Nash equilibria and sets of action profiles that are attracting with high probability, and we also introduce the notion of coherence, a game-theoretic property that includes strict and sharp equilibria, and which leads to convergence in finite time. Importantly, our analysis applies to both oracle-based and bandit, payoff-based methods — that is, when players only observe their realized payoffs.

On the discrete-time origins of the replicator dynamics: From convergence to instability and chaos

We consider in 37 three distinct discrete-time models of learning and evolution in games: a biological model based on intra-species selective pressure, the dynamics induced by pairwise proportional imitation, and the exponential / multiplicative weights (EW) algorithm for online learning. Even though these models share the same continuous-time limit — the replicator dynamics — we show that second-order effects play a crucial role and may lead to drastically different behaviors in each model, even in very simple, symmetric $2\times 2$ games. Specifically, we study the resulting discrete-time dynamics in a class of parameterized congestion games, and we show that (i) in the biological model of intra-species competition, the dynamics remain convergent for any parameter value; (ii) the dynamics of pairwise proportional imitation exhibit an entire range of behaviors for larger time steps and different equilibrium configurations (stability, instability, and even Li-Yorke chaos); while (iii) in the EW algorithm, increasing the time step (almost) inevitably leads to chaos (again, in the formal, Li-Yorke sense). This divergence of behaviors comes in stark contrast to the globally convergent behavior of the replicator dynamics, and serves to delineate the extent to which the replicator dynamics provide a useful predictor for the long-run behavior of their discrete-time origins.

Nested replicator dynamics, nested logit choice, and similarity-based learning

We consider in 16 a model of learning and evolution in games whose action sets are endowed with a partition-based similarity structure intended to capture exogenous similarities between strategies. In this model, revising agents have a higher probability of comparing their current strategy with other strategies that they deem similar, and they switch to the observed strategy with probability proportional to its payoff excess. Because of this implicit bias toward similar strategies, the resulting dynamics - which we call the nested replicator dynamics - do not satisfy any of the standard monotonicity postulates for imitative game dynamics; nonetheless, we show that they retain the main long-run rationality properties of the replicator dynamics, albeit at quantitatively different rates. We also show that the induced dynamics can be viewed as a stimulus-response model in the spirit of Erev & Roth (1998), with choice probabilities given by the nested logit choice rule of Ben-Akiva (1973) and McFadden (1978). This result generalizes an existing relation between the replicator dynamics and the exponential weights algorithm in online learning, and provides an additional layer of interpretation to our analysis and results.

A geometric decomposition of finite games: Convergence vs. recurrence under exponential weightsky

In view of the complexity of the dynamics of learning in games, we seek to decompose a game into simpler components where the dynamics' long-run behavior is well understood. A natural starting point for this is Helmholtz's theorem, which decomposes a vector field into a potential and an incompressible component. However, the geometry of game dynamics - and, in particular, the dynamics of exponential / multiplicative weights (EW) schemes - is not compatible with the Euclidean underpinnings of Helmholtz's theorem. This leads us to consider in 16 a specific Riemannian framework based on the so-called Shahshahani metric, and introduce the class of incompressible games, for which we establish the following results: First, in addition to being volume-preserving, the continuous-time EW dynamics in incompressible games admit a constant of motion and are Poincar$\setminus$'e recurrent — i.e., almost every trajectory of play comes arbitrarily close to its starting point infinitely often. Second, we establish a deep connection with a well-known decomposition of games into a potential and harmonic component (where the players' objectives are aligned and anti-aligned respectively): a game is incompressible if and only if it is harmonic, implying in turn that the EW dynamics lead to Poincaré recurrence in harmonic games.

No-regret learning in harmonic games: Extrapolation in the face of conflicting interests

The long-run behavior of multi-agent learning — and, in particular, no-regret learning — is relatively well-understood in potential games, where players have aligned interests. By contrast, in harmonic games — the strategic counterpart of potential games, where players have conflicting interests — very little is known outside the narrow subclass of 2-player zero-sum games with a fully-mixed equilibrium. In 23, we seek to partially fill this gap by focusing on the full class of (generalized) harmonic games and examining the convergence properties of follow-the-regularized-leader (FTRL), the most widely studied class of no-regret learning schemes. As a first result, we show that the continuous-time dynamics of FTRL are Poincaré recurrent, that is, they return arbitrarily close to their starting point infinitely often, and hence fail to converge. In discrete time, the standard, "vanilla" implementation of FTRL may lead to even worse outcomes, eventually trapping the players in a perpetual cycle of best-responses. However, if FTRL is augmented with a suitable extrapolation step - which includes as special cases the optimistic and mirror-prox variants of FTRL — we show that learning converges to a Nash equilibrium from any initial condition, and all players are guaranteed at most $O\left(1\right)$ regret. These results provide an in-depth understanding of no-regret learning in harmonic games, nesting prior work on 2-player zero-sum games, and showing at a high level that harmonic games are the canonical complement of potential games, not only from a strategic, but also from a dynamic viewpoint.

Accelerated regularized learning in finite N-person games

Last, motivated by the success of Nesterov's accelerated gradient algorithm for convex minimization problems, we examine in 25 whether it is possible to achieve similar performance gains in the context of online learning in games. To that end, we introduce a family of accelerated learning methods, which we call "follow the accelerated leader" (FTXL), and which incorporates the use of momentum within the general framework of regularized learning — and, in particular, the exponential/multiplicative weights algorithm and its variants. Drawing inspiration and techniques from the continuous-time analysis of Nesterov's algorithm, we show that FTXL converges locally to strict Nash equilibria at a superlinear rate, achieving in this way an exponential speed-up over vanilla regularized learning methods (which, by comparison, converge to strict equilibria at a geometric, linear rate). Importantly, FTXL maintains its superlinear convergence rate in a broad range of feedback structures, from deterministic, full information models to stochastic, realization-based ones, and even when run with bandit, payoff-based information, where players are only able to observe their individual realized payoffs.

Theoretical Guarantees and Improvement of Large Dimensional Multi-Task Semi-Supervised Classification

In the field of machine learning, the specific subfield of deep learning has gathered particular interest in the last decade. If deep learning has allowed quick and significant progress in a wide range of fields, this progress has been made at the expense of interpretability, accessibility, robustness and flexibility, not to mention the colossal energy consumption implied by the training of such algorithms. On the contrary, the thesis of Victor Leger 32 aims to open the path to all-encompassing flexible tools for classification problems, buttressed on elementary machine learning notions and rather basic mathematical tools. This thesis conducts a large dimensional study of a simple yet quite versatile classification model, encompassing at once multi-task and semi-supervised learning, and taking into account uncertain labeling. Using tools from random matrix theory, the asymptotics of some key functionals are characterized, which allows on the one hand to predict the performances of the proposed algorithm, and on the other hand to reveal some counter-intuitive guidance on how to use it efficiently. The model, powerful enough to provide good performance guarantees, is also straightforward enough to provide strong insight into its behavior. The resulting algorithm is also compared to an optimal bound derived from statistical physics, which gives a lower bound of the least achievable probability of misclassification for a given problem. This bound is computed in the extended case of uncertain labeling, and is used to evaluate the performances of the algorithm.

Theoretical performance analysis applied to non-convex and fair algorithms using Random Matrix Theory

In the thesis of Charles Sejourne33, we study theoretically the performance of well-known Machine Learning algorithms (t-SNE and LS-SVM). For the first algorithm, we study an asymptotic characterization of the critical points of the optimization problem of the cousin of t-SNE, Symmetric SNE, in a large-dimensional setting. For the second algorithm, we study theoretically the behavior of LS-SVM when adding fairness constraints aiming at making the algorithm more fair.

Performance Gaps in Multi-view Clustering under the Nested Matrix-Tensor Model

We study in 22 the estimation of a planted signal hidden in a recently introduced nested matrix-tensor model, which is an extension of the classical spiked rank-one tensor model, motivated by multi-view clustering. Prior work has theoretically examined the performance of a tensor-based approach, which relies on finding a best rank-one approximation, a problem known to be computationally hard. A tractable alternative approach consists in computing instead the best rank-one (matrix) approximation of an unfolding of the observed tensor data, but its performance was hitherto unknown. We quantify here the performance gap between these two approaches, in particular by deriving the precise algorithmic threshold of the unfolding approach and demonstrating that it exhibits a BBP-type transition behavior. This work is therefore in line with recent contributions which deepen our understanding of why tensor-based methods surpass matrix-based methods in handling structured tensor data.

A Random Matrix Approach to Low-Multilinear-Rank Tensor Approximation

In 39, we present a comprehensive understanding of the estimation of a planted low-rank signal from a general spiked tensor model near the computational threshold. Relying on standard tools from the theory of large random matrices, we characterize the large-dimensional spectral behavior of the unfoldings of the data tensor and exhibit relevant signal-to-noise ratios governing the detectability of the principal directions of the signal. These results allow to accurately predict the reconstruction performance of truncated multilinear SVD (MLSVD) in the non-trivial regime. This is particularly important since it serves as an initialization of the higher-order orthogonal iteration (HOOI) scheme, whose convergence to the best low-multilinear-rank approximation depends entirely on its initialization. We give a sufficient condition for the convergence of HOOI and show that the number of iterations before convergence tends to 1 in the large-dimensional limit.

Asymptotic Gaussian Fluctuations of Eigenvectors in Spectral Clustering

The performance of spectral clustering relies on the fluctuations of the entries of the eigenvectors of a similarity matrix, which has been left uncharacterized until now. In 13, we show that the signal + noise structure of a general spike random matrix model is transferred to the eigenvectors of the corresponding Gram kernel matrix and the fluctuations of their entries are Gaussian in the large-dimensional regime. This CLT-like result was the last missing piece to precisely predict the classification performance of spectral clustering. The proposed proof is very general and relies solely on the rotational invariance of the noise. Numerical experiments on synthetic and real data illustrate the universality of this phenomenon.

Efficiency and Fairness in Matching Problems

In the thesis of Rémi Castera 31, we study matching models, i.e., models based on a bipartite graph where the objective is to find a set of edges in the graph (called a matching) that satisfies or maximizes some objective. In the basic setup, the objective is to find the largest possible set of edges. When the vertices of the graph are agents with preferences over the possible partners, we look for matchings that are deemed stable, while trying to maximize the satisfaction of the agents. We assume that vertices on one side of the graph are divided into groups, those groups could represent different demographics, that we would like to be treated fairly when choosing a matching. In this thesis, we look into various definitions of fairness towards those groups (a concept called group fairness), and which parameters of each studied model play a role in the existence or the optimality of a fair matching. In particular, we study the trade-off between fairness and efficiency, defined as the size of the matching when there are no preferences, or the satisfaction of agents when there are preferences. In the setting with no preferences, we propose an original geometric representation of the problem that allows us to give conditions for the existence of a matching that is maximal and fair, and when it does not exist we provide tight bounds on the ratio between the size of the largest matching and the size of the largest fair matching (we call this ratio the Price of Fairness). In the setting with preferences, that we model as a college admission problem with students on one side an colleges on the other side, we study the role of the correlation between colleges' rankings of students. We show that correlation improves the efficiency of the stable matching. However when different groups have different levels of correlation, groups with higher correlation have higher rates of students remaining unassigned, even when each college's individual ranking is completely fair towards each group. We also show that when colleges' rankings are fair, there is no trade-off between efficiency and fairness.

Correlation of Rankings in Matching Markets

The latest results have been submitted in 35, where we study the role of correlation in matching, where multiple decision-makers simultaneously face selection problems from the same pool of candidates. We propose a model in which decision-makers have varying information on candidates from different sociodemographic groups when evaluating and ranking them, thus leading to varying correlations among candidates’ priority scores. Such differential correlation arises, for example, when the cost of information acquisition, decision-maker preferences, or the prevalence of selection criteria vary across sociodemographic groups. We show that a lower correlation for one of the groups worsens the outcome for all groups, thus leading to efficiency loss. Moreover, the proportion of students from a given group who remain unmatched is increasing in its own correlation level. This implies that it is advantageous to belong to the low-correlation group. Finally, we extend the extent tie-breaking literature to multiple priority classes and intermediate levels of correlation. Overall, our results point to a previously overlooked systemic source of group inequalities in school, university, and job admissions.

Quick or cheap? Breaking points in dynamic markets

In 15, we examine two-sided markets where players arrive stochastically over time. The cost of matching a client and provider is heterogeneous, and the distribution of costs — but not their realization — is known. In this way, a social planner is faced with two contending objectives:(a) to reduce the players’ waiting time before getting matched; and (b) to reduce matching costs. In this paper, we aim to understand when and how these objectives are incompatible. We identify two regimes dependent on the ‘speed of improvement’ of the cost of matching with respect to market size. One regime results in a quick or cheap dilemma without ‘free lunch’: there exists no clearing schedule that is simultaneously optimal along both objectives. In that regime, we identify a unique breaking point signifying a stark reduction in matching cost contrasted by an increase in waiting time. The other regime features a window of opportunity in which free lunch can be achieved. Which scheduling policy is optimal depends on the heterogeneity of match costs. Under limited heterogeneity, e.g., when there is a finite number of possible match costs, greedy scheduling is approximately optimal, in line with the related literature. However, with more heterogeneity greedy scheduling is never optimal. Finally, we analyze a particular model where match costs are exponentially distributed and show that it is at the boundary of the no-free-lunch regime. We then characterize the optimal clearing schedule for varying social planner desiderata.

The representation dynamic and the “normalization” of group differences

Abstract Intergroup inequality has been linked to differing norms of economic participation among groups. In 8, we present a theory of endogenous identity-specific norms in which the larger a group’s representation in an economic activity, the more the activity is deemed “normal” or “appropriate” for its members. This representation dynamic can arise from behavioral heuristics or be created by informational technologies such as generative artificial intelligence. Through it, the economic underrepresentation of a group becomes “normalized,” resulting in more severe inequality than in standard models. Equality of opportunity almost never results in equal outcomes, even when groups have the same productivity. Minorities and historically marginalized groups tend to be underrepresented. However, minorities with greater productivity and/or weaker group identification can become overrepresented, and even dominant. When there are multiple career stages, underrepresentation can escalate at senior levels long after “glass ceilings” have disappeared. Underrepresentation disappears as economic returns rise and/or group identification weakens.

Intersectionality: Affirmative Action with Multidimensional Identities

Studying the design of affirmative action policies when identities are multidimensional, we provide in 9 a formal demonstration of the importance of intersectionality. Prevailing affirmative action policies are based only on one identity dimension (e.g., race, gender, socioeconomic class). We find that any such nonintersectional policy can almost never achieve a representative outcome. In fact, nonintersectional policies often increase the underrepresentation of underrepresented groups in a manner undetected by standard measures. Examples based on race and gender reveal significant hidden inequality arising from nonintersectional policies. We show how to construct intersectional policies that achieve proportional representation.

Booléens en programmation : une analyse à destination des enseignants

The notion of boolean is fundamental in computer science. Even if it seems simple at first sight, its introduction in the first stages of programming education reveals a number of difficulties related to the fact that it is linked to several general concepts of computer science: data types, truth values, invariants, control structures... Starting from this observation, we propose in 18 a reflection on the role of booleans in programming. We elaborate on some points concerning possible “good practices”, especially in the context of computer science teaching. In particular, we focus on boolean as a data type and on the main control structures using booleans. We also discuss the general notion of boolean expression used in programming. Finally through a few examples, we illustrate some typical uses of boolean variables.

Tele-vision: unplugged computing at the service of the concept of information

Computer science teaching, from elementary school through to high school, is structured around the “four concepts or facets” of computing and digital objects: information, algorithms, programming languages and computing machines. The aim of the Tele-vision activity analyzed in 17 is to introduce the fundamental concepts of the “information” facet through a sequence of unplugged activities. The activity involves the transmission of images from one student to another, using two-colored tokens. Using the tokens, then the faces of a dice to materialize the information, students agree on a code, encoding, transmitting and decoding the information. They evaluate the entire transmission protocol (correctness, efficiency, etc.). A reflective analysis of experiments carried out in Cycle 3 (6th grade) is proposed to identify the knowledge taught and the skills involved. Finally, the activity is considered from a broader perspective (other levels or other concepts).

10.1.1 Inria associate team not involved in an IIL or an international program

10.2.1 Visits of international scientists

Manu Gupta visited Inria for a total duration of one month in June 2024. Deborah Hendrych visited Inria for a duration of one month in October 2024.

10.2.2 Visits to international teams

ANR

• ANR REFINO (JCJC 2020-2025)$☆$

  Refined Mean Field Optimization[250K€]

  REFINO is an ANR starting grant (JCJC) coordinated by Nicolas Gast. The main objective on this project is to provide an innovative framework for optimal control of stochastic distributed agents. Restless bandit allocation is one particular example where the control that can be sent to each arm is restricted to an on/off signal. The originality of this framework is the use of refined mean field approximation to develop control heuristics that are asymptotically optimal as the number of arms goes to infinity and that also have a better performance than existing heuristics for a moderate number of arms. As an example, we will use this framework in the context of smart grids, to develop control policies for distributed electric appliances.

• ANR FAIRPLAY (JCJC 2021-2025)$☆$

  Fair algorithms via game theory and sequential learning[245K€]

  FAIRPLAY is an ANR starting grant (JCJC) coordinated by Patrick Loiseau. Machine learning algorithms are increasingly used to optimize decision making in various areas, but this can result in unacceptable discrimination. The main objective of this project is to propose an innovative framework for the development of learning algorithms that respect fairness constraints. While the literature mostly focuses on idealized settings, the originality of this framework and central focus of this project is the use of game theory and sequential learning methods to account for constraints that appear in practical applications: strategic and decentralized aspects of the decisions and the data provided and absence of knowledge of certain parameters key to the fairness definition.

11.1.1 Scientific events: organisation

• Arnaud Legrand co-organized with five other colleagues the second Meeting days of the French network for reproducible research in Grenoble, France, March 2024, which has attracted about a hundred of researchers. The aim of these days was to provide an overview of the state of reproducibility in scientific research in France, taking into account the diversity of disciplines and practices.

11.1.2 Scientific events: selection

11.1.3 Journal

11.1.4 Invited talks

• Bruno Gaujal was invited to present his works at the following events:
  • "Machine Learning and Mean Field Games" Seminar series (May, 2024).
  • Recent trends in scheduling Theory (June 2024)
  • scheduling in Aussois (July 20204)
  • Keynote at Conf. Reinforcement Learning in Stochastic Networks (June 2024)
  • Journées MAS (Nov. 2024)
  • Atelier d’eval. de Perf. (table ronde) (Dec. 2024)
• Nicolas Gast was invited to present his work at the "13ème Atelier en Évaluation des Performances" (workshop AEP13, Toulouse), at the conference NetGCOOP 2024, and at the workshop RL4SN (Reinforcement Learning for Stochastic Networks).
• Jonatha Anselmi was invited to present his work on load-balancing and auto-scaling at the "13ème Atelier en Évaluation des Performances" (Toulouse)
• Arnaud Legrand was invited to give lectures and keynotes on Reproducible Research and Open Science on the following occasions:
  • M1 students in computer science at UGA (Dec. 2024): Reproducible Research and Computer Science
  • Theory days on Computational tools in physics : performances vs. reproducibility at Toulouse (Nov. 2023): Numerical/Software Chaos and Reproducibility Issues in HPC
  • 52nd ORAP Forum on Reproductiblité et HPC at Paris (Mar. 2024): Presentation of the French Reproducible Research Network and Reproducibility Issues and Publication Evolutions (in HPC).
  • RSD Winter School at Le Pleynet (Feb. 2024): Reproducible Research and Computer Science.
  • L3 students of ENS Lyon at Le Pleynet (Jan. 2024): Reproducible Research and Computer Science.
• Panayotis Mertikopoulos was invited to give a tutorial at the following events:
  • EPFL-ETHZ Summer School on Multi-Agent Reinforcement Learning, Lausanne, CH
  • Games and Artificial Intelligence Multidisciplinary Summer School, Metz, FR
• Panayotis Mertikopoulos was invited to give a talk in the following conferences:
  • HMS 2024–The 2024 Conference of the Hellenic Mathematical Society, Olympia, GR
  • One World Optimization Seminar in Vienna, Vienna, AT
  • SOLACE Workshop on Learning in Games, Toulouse, FR
  • ACAC 2024–Athens Colloquium on Algorithms and Complexity, Athens, GR
  • Moroccan Game Theory Days, Rabat, MC
• Panayotis Mertikopoulos was invited to give a talk in the following universities and research institutes:
  • Institute of Applied and Computational Mathematics, Herakleion, GR
  • Paris Game Theory Seminar (Institut Henri Poincaré), Paris, FR
  • Algorithmic Learning in Games Seminar, Online
  • GAIA/DATA Seminar, Grenoble, FR
• Mathieu Besançon gave an invited full talk at the Mixed-Integer Programming Workshop (University of Kentucky), and gave a lecture at the Computational Optimization at Work summer school at the Zuse Institute Berlin.

11.1.5 Leadership within the scientific community

• Vincent Danjean , Guillaume Huard , Arnaud Legrand , and Jean-Marc Vincent, are involved in the WP5 (Performance analysis and prediction) of the ExaSoft pillar (High Performance Computing software and tools) of the PEPR NumPEx (Numérique Hautes Performances pour l'Exascale).
• Panayotis Mertikopoulos is the scientific coordinator of the PEPR IA projet ciblé (acceleration grant) FOUNDRY: Foundations of robustness and reliability in artificial intelligence. The project has a total budget of 5M€ and involves five research teams across France (POLARIS in Grenoble, the Inria teams SCOOL and FAIRPLAY, Dauphine and IMT in Paris, and ENS Lyon).
• Jean-Marc Vincent is a member of the scientific committee of the CIST.
• Jean-Marc Vincent is vice-head of the SIF, adjunct on teaching. In this context he is in charge of the organization of the annual meeting on education in computer science.

11.1.6 Scientific expertise

• Nicolas Gast was co-chair of the ACM SIGMETRICS "Student Research Competition".
• Jean-Marc Vincent is a scientific expert in EFELIA-MIAI.

11.1.7 Research administration

• Mathieu Besançon was a member of the hiring committee for a fixed-term Maître-Assistant at IMT Mines Albi.
• Vincent Danjean is a member of the Conseil d'Administration of Grenoble-INP.
• Bruno Gaujal was president of the jury for Mcf hiring in ENSGI (Grenoble).
• Nicolas Gast is vice-head of the Labex EnergyAlps that federates the community working on electrical energy in Grenoble.
• Nicolas Gast is vice-head of the école doctorale MSTII (the doctoral school managing PhD students in computer science and mathemathics at Univ. Grenoble Alpes).
• Arnaud Legrand is a member of the Section 6 of the CoNRS.
• Arnaud Legrand is head of the SRCPR axis of the LIG and a member of LIG bureau.
• Arnaud Legrand is a member of Comité Scientique of the Inria Grenoble.
• Florence Perronin is a member of the QVT team of the LIG.
• Jean-Marc Vincent was a member of the jury for Mcf hiring in Univ. Nancy.
• Jean-Marc Vincent is the head of the evaluation committee for education in AI of the MIAI chaire.

11.2.1 Teaching

• Jonatha Anselmi teaches Probabilités et simulation (32h) and Évaluation de performances (32h) at PolyTech Grenoble.
• Mathieu Besançon teaches half of the Advanced Models and Methods of Operations Research at the M2 ORCO (UGA).
• Vincent Danjean teaches the Operating Systems, Programming Languages, Algorithms, Computer Science and Mediation lectures in L3, M1 and Polytech Grenoble.
• Vincent Danjean organized with J.M. Vincent a complementary training for high school professors to teach computer science.
• Nicolas Gast teaches the Reinforcement learning part of the M2 course Mathematical foundations of machine learning at the M2 MOSIG (Grenoble).
• Bruno Gaujal teaches Optimisation under uncertainties (18h) at the M2 ORCO (UGA).
• Bruno Gaujal and Nicolas Gast teach Markov Decision Process and Reinforcement Learning (32h in total) at the M2 Info (ENS Lyon).
• Nicolas Gast is responsible of the cours "Introduction au Machine Learning" that is an optional course of the third year or the "licence informatique" at Univ. Grenoble Alpes.
• Guillaume Huard is responsible of L3 Info and of the Licence Info.
• Guillaume Huard is responsible of the courses UNIX & C programming in the L1 and L3 INFO, of Object Oriented and Event-Driven Programming in the L3 INFO, and of the Objet Oriented Design in M1 INFO.
• Arnaud Legrand and Jean-Marc Vincent teach the transversal Scientific Methodology and Empirical Evaluation lecture (36h) at the M2 MOSIG (UGA).
• The 3rd edition of the MOOC of Arnaud Legrand , K. Hinsen and C. Pouzat on Reproducible Research: Methodological Principles for a Transparent Science is still running. Over the 3 editions (Oct.-Dec. 2018, Apr.-June 2019, March 2020 - end of 2024), more than 22,800 persons have followed this MOOC and about 2600 certificates of achievement have been delivered. More than half of participants are PhD students and about 10% are undergraduates.
• The 1st edition of the MOOC of Arnaud Legrand , K. Hinsen and C. Pouzat on Reproducible Research II: Practices and tools for managing computations and data has been launched from May 2024 to October 2024. It has has attracted 2,000 persons and is the result of more than 3 years of hard work.
• Florence Perronin teaches Programming Languages in L1.
• Florence Perronin is a member of the conseil de perfectionnement of the Mathematics license.
• Jean-Marc Vincent is in charge of the coordination of the training of high school teachers in computer science (NSI) in Grenoble.
• Jean-Marc Vincent teaches Algorithms and Probabilities at the L3, UGA.
• Jean-Marc Vincent teaches Statistical Models and Litterate Programming at the L3 MIAGE, UGA.
• Jean-Marc Vincent teaches Mathematics for Computer Science at the M1 MOSIG, UGA.
• Jean-Marc Vincent participates to the Histoire de l’informatique lecture at the ENSIMAG.
• Panayotis Mertikopoulos taught a graduate course on continuous optimization in the University of Athens.

11.2.2 Supervision

Bruno Gaujal is member of the CSI of Adrienne Tuynman (Univ. Lille) and Vittorio Puricelli (Univ. Toulouse)

11.2.3 Juries

• Nicolas Gast was member of the PhD committee of Younes Ben Mazziane (Univ. Sofia Antopolis and Inria): Probabilistic analysis for caching.
• Nicolas Gast was member of the jury for the "Prix de thèse PGMO" 2024.
• Arnaud Legrand was a reviewer for the PhD of Maël Madon (Univ. de Toulouse): Digital Sufficiency in Data Centers : Studying the Impact of User Behaviors.
• Arnaud Legrand was president of the PhD committee of Adrien Berthelot (ÉNS Lyon): L'empreinte environnementale complète d'un usage numérique : contribution à l'analyse de cycle de vie de service numérique .
• Panayotis Mertikopoulos was an external reviewer for the PhD thesis of Mohammad Reza Karimi (ETH Zürich) on Stochastic Approximation on Riemannian Manifolds and the Space of Measures

11.3.1 Specific official responsibilities in science outreach structures

• Jean-Marc Vincent is particularly involved in the teaching of computer science at the national level.
  • He co-animates the national group infosansordi (unplugged computer science).
  • He participates to the training of high school computer science teachers (NSI) and he is preparing a new training on programming methods.
  • He also co-organizes series of seminars for high school computer science teachers.
  • He is a member of the national inter-IREM group on computer science and writes leaflets for high school computer science teachers.
• Jean-Marc Vincent is a member of the scientific committee of Territoires de Sciences, which in charge of popularization in the Grenoble area.
• Jean-Marc Vincent is a member of the committee of the national Trophée NSI.
• Jean-Marc Vincent is in charge of relationships on Education between Inria Grenoble and the Grenoble Rectorat.
• Jean-Marc Vincent is in the comité de pilotage du plan national formation in computer science for middle schools and high schools.
• Jean-Marc Vincent is in the comité de pilotage du plan national formation in unplugged computer science (informatique débranchée) for elementary schools.

11.3.2 Participation in Live events

• Jean-Marc Vincent has organized 4 conferences at the Kateb Yacine library for general audience: Le numérique en questions, with Inria, UGA and the Grenoble city.
• Jean-Marc Vincent has organized 2 days of the conference MathC2+ toward middle school and high school students with Inria and UGA.

International journals

• 1 articleJ.Jonatha ANSELMI and J.Josu Doncel. Dispatching and scheduling multiserver jobs for throughput optimality.ACM SIGMETRICS Performance Evaluation Review2024, 1-5In press. HALback to text
• 2 articleJ.Jonatha Anselmi. Asynchronous Load Balancing and Auto-scaling: Mean-Field Limit and Optimal Design.IEEE/ACM Transactions on Networking2024, 1-12HALDOIback to text
• 3 articleJ.Jonatha Anselmi and J.Josu Doncel. Balanced Splitting: A Framework for Achieving Zero-wait in the Multiserver-job Model.IEEE Transactions on Parallel and Distributed SystemsSeptember 2024, 1-12In press. HALDOIback to text
• 4 articleJ.Jonatha Anselmi and J.Josu Doncel. Load Balancing with Job-Size Testing: Performance Improvement or Degradation?ACM Transactions on Modeling and Performance Evaluation of Computing Systems2024, 1-25HALDOIback to text
• 5 articleJ.Jonatha Anselmi, B.Bruno Gaujal and L.-S.Louis-Sébastien Rebuffi. Learning Optimal Admission Control in Partially Observable Queueing Networks.Queueing SystemsJune 2024, 1-48HALDOIback to text
• 6 articleW.Waïss Azizian, F.Franck Iutzeler, J.Jérôme Malick and P.Panayotis Mertikopoulos. The rate of convergence of Bregman proximal methods: Local geometry vs. regularity vs. sharpness.SIAM Journal on Optimization3432024, 2440-2471HALDOIback to text
• 7 articleM.Mathieu Besançon, M.Miguel Anjos and L.Luce Brotcorne. Robust bilevel optimization for near-optimal lower-level solutions.Journal of Global Optimization904July 2024, 813-842HALDOIback to text
• 8 articleJ.-P.Jean-Paul Carvalho and B.Bary Pradelski. The representation dynamic and the “normalization” of group differences.Journal of Law, Economics, and OrganizationJune 2024, 1-28HALDOIback to text
• 9 articleJ.-P.Jean-Paul Carvalho, B.Bary Pradelski and C.Cole Williams. Intersectionality: Affirmative Action with Multidimensional Identities.Management ScienceSeptember 2024HALDOIback to text
• 10 articleF.Federica Filippini, J.Jonatha ANSELMI, D.Danilo Ardagna and B.Bruno Gaujal. A Stochastic Approach for Scheduling AI Training Jobs in GPU-based Systems.IEEE Transactions on Cloud Computing1212024, 53-69HALDOIback to text
• 11 articleN.Nicolas Gast and B.Benny van Houdt. Approximations to Study the Impact of the Service Discipline in Systems with Redundancy.Proceedings of the ACM on Measurement and Analysis of Computing Systems 81March 2024, 1-32HALDOIback to text
• 12 articleB.Bruno Gaujal, A.Alain Girault and S.Stéphan Plassart. An MDP-Based Solution for the Energy Minimization of Non-Clairvoyant Hard Real-Time Systems.Real-Time SystemsDecember 2024, 47HALDOIback to textback to text
• 13 articleH.Hugo Lebeau, F.Florent Chatelain and R.Romain Couillet. Asymptotic Gaussian Fluctuations of Eigenvectors in Spectral Clustering.IEEE Signal Processing Letters312024, 1920-1924HALDOIback to text
• 14 articleP.Panayotis Mertikopoulos, Y.-P.Ya-Ping Hsieh and V.Volkan Cevher. A unified stochastic approximation framework for learning in games.Mathematical Programming203January 2024, 559-609HALDOIback to text
• 15 articleP.Panayotis Mertikopoulos, H. H.Heinrich H Nax and B. S.Bary S R Pradelski. Quick or cheap? Breaking points in dynamic markets.Journal of Mathematical Economics112June 2024, 102987HALDOIback to text
• 16 articleP.Panayotis Mertikopoulos and W. H.William H Sandholm. Nested replicator dynamics, nested logit choice, and similarity-based learning.Journal of Economic Theory220September 2024, 105881HALDOIback to textback to text
• 17 articleJ.-M.Jean-Marc Vincent and M.Maryline Althuser. La Télé-vision : l’informatique débranchée au service du concept d’information.Petit x120September 2024, 9-38HALback to text

National journals

• 18 articleS.Sylvie Alayrangues, O.Olivier Baudon, E.Emmanuel Beffara, R.Ronan Charpentier, S.Sébastien Daniel, C.Christophe Declercq, A.Aslı Grimaud, S.Sébastien Hoarau, A.Anne Héam, P.Philippe Marquet, J.-C.Jean-Christophe Masseron, A.Antoine Meyer, M.Malika More, F.Florence Nény, C.Cécile Prouteau, J.-M.Jean-Marc Vincent, E.Emmanuel Volte and N.Nathalie Weibel. Booléens en programmation : une analyse à destination des enseignants.Recherches et recherches-actions en didactique de l'informatique12024, 1-33HALback to text

International peer-reviewed conferences

• 19 inproceedingsS.Sebastian Allmeier and N.Nicolas Gast. Computing the Bias of Constant-step Stochastic Approximation with Markovian Noise.NeurIPS 2024 -38th Annual Conference on Neural Information Processing SystemsVancouver, Canada2024, 1-23HALback to text
• 20 inproceedingsW.Waïss Azizian, F.Franck Iutzeler, J.Jérôme Malick and P.Panayotis Mertikopoulos. What is the long-run distribution of stochastic gradient descent? A large deviations analysis.ICML 2024 - 41st International Conference on Machine LearningVienna, AustriaJuly 2024, 1-70HALback to text
• 21 inproceedingsA.Andreas Kontogiannis, V.Vasilis Pollatos, S.Sotiris Kanellopoulos, P.Panayotis Mertikopoulos, A.Aris Pagourtzis and I.Ioannis Panageas. The computational complexity of finding second-order stationary points.ICML 2024 - 41st International Conference on Machine LearningVienna, AustriaJuly 2024HALback to text
• 22 inproceedingsH.Hugo Lebeau, M.Mohamed El Amine Seddik and J. H.José Henrique de M Goulart. Performance Gaps in Multi-view Clustering under the Nested Matrix-Tensor Model.ICLR 2024 - 12th International Conference on Learning RepresentationsWien, Austria2024, 1-29HALback to text
• 23 inproceedingsD.Davide Legacci, P.Panayotis Mertikopoulos, C.Christos Papadimitriou, G.Georgios Piliouras and B. S.Bary S R Pradelski. No-regret learning in harmonic games: Extrapolation in the face of conflicting interests.Proceedings of the 38th International Conference on Neural Information Processing SystemsNeurIPS 2024 - 38th Conference on Neural Information Processing SystemsVancouver, Canada2024, 1-36HALback to text
• 24 inproceedingsD.Davide Legacci, P.Panayotis Mertikopoulos and B.Bary Pradelski. A geometric decomposition of finite games: Convergence vs. recurrence under exponential weights.ICML 2024 - 41st International Conference on Machine LearningVienna, AustriaJuly 2024HAL
• 25 inproceedingsK.Kyriakos Lotidis, A.Angeliki Giannou, P.Panayotis Mertikopoulos and N.Nicholas Bambos. Accelerated regularized learning in finite N-person games.Proceedings of the 38th International Conference on Neural Information Processing SystemsNeurIPS 2024 - 38th Conference on Neural Information Processing SystemsVancouver, Canada2024HALback to text
• 26 inproceedingsG.Gioni Mexi, S.Somayeh Shamsi, M.Mathieu Besançon and P.Pierre Le Bodic. Probabilistic Lookahead Strong Branching via a Stochastic Abstract Branching Model.Integration of Constraint Programming, Artificial Intelligence, and Operations ResearchCPAIOR 2024 - 21st International Conference on Integration of Constraint Programming, Artificial Intelligence, and Operations Research14743Lecture Notes in Computer ScienceUppsala, SwedenSpringer Nature SwitzerlandMay 2024, 56-73HALDOIback to text

Conferences without proceedings

• 27 inproceedingsK.Kartikey Sharma, D.Deborah Hendrych, M.Mathieu Besançon and S.Sebastian Pokutta. Network Design for the Traffic Assignment Problem with Mixed-Integer Frank-Wolfe.INFORMS Optimization Society ConferenceHouston, United StatesMarch 2024HALback to text

Edition (books, proceedings, special issue of a journal)

• 28 proceedingsSolving the Optimal Experiment Design Problem with Mixed-Integer Convex Methods.22nd International Symposium on Experimental Algorithms (SEA 2024)301301Schloss Dagstuhl -- Leibniz-Zentrum für Informatik2024, 16:1--16:22HALDOIback to text

Doctoral dissertations and habilitation theses

• 29 thesisS.Sebastian Allmeier. Mean Field Methods for Heterogeneous and Coupled Systems.Université Grenoble Alpes [2020-....]April 2024HALback to text
• 30 thesisV.Victor Boone. Optimal Regrets in Markov Decision Processes.UGA (Université Grenoble Alpes)November 2024HALback to text
• 31 thesisR.Rémi Castera. Efficiency and Fairness in Matching Problems.UGA (Université Grenoble Alpes)October 2024HALback to text
• 32 thesisV.Victor Leger. Theoretical guarantees and improvement of large dimensional multi-task semi-supervised classification.UGA (Université Grenoble Alpes)November 2024HALback to text
• 33 thesisC.Charles Sejourne. Theoretical performance analysis applied to non-convex and fair algorithms using Random Matrix Theory.UGA (Université Grenoble Alpes)December 2024HALback to text

Reports & preprints

• 34 miscS.Suresh Bolusani, M.Mathieu Besançon, K.Ksenia Bestuzheva, A.Antonia Chmiela, J.João Dionísio, T.Tim Donkiewicz, J.Jasper van Doornmalen, L.Leon Eifler, M.Mohammed Ghannam, A.Ambros Gleixner, C.Christoph Graczyk, K.Katrin Halbig, I.Ivo Hedtke, A.Alexander Hoen, C.Christopher Hojny, R.Rolf van der Hulst, D.Dominik Kamp, T.Thorsten Koch, K.Kevin Kofler, J.Jurgen Lentz, J.Julian Manns, G.Gioni Mexi, E.Erik Mühmer, M. E.Marc E. Pfetsch, F.Franziska Schlösser, F.Felipe Serrano, Y.Yuji Shinano, M.Mark Turner, S.Stefan Vigerske, D.Dieter Weninger and L.Lixing Xu. The SCIP Optimization Suite 9.0.February 2024HALback to text
• 35 miscR.Rémi Castera, P.Patrick Loiseau and B.Bary Pradelski. Correlation of Rankings in Matching Markets.February 2024HALback to text
• 36 miscY.Yohann Chasseray, M.Mathieu Besançon, E.Eva Petitdemange and X.Xavier Lorca. Optimisation models for the design of multiple self-consumption loops in semi-rural areas.2024HALDOIback to text
• 37 miscF.Fryderyk Falniowski and P.Panayotis Mertikopoulos. On the discrete-time origins of the replicator dynamics: From convergence to instability and chaos.February 2024HALback to text
• 38 miscN.Nicolas Gast, B.Bruno Gaujal and C.Chen Yan. Reoptimization Nearly Solves Weakly Coupled Markov Decision Processes.2024HALback to text
• 39 miscH.Hugo Lebeau, F.Florent Chatelain, R.Romain Couillet and R.Romain Couillet. A Random Matrix Approach to Low-Multilinear-Rank Tensor Approximation.June 2024HALback to text
• 40 miscT.Tianyi Lin, P.Panayotis Mertikopoulos and M. I.Michael I. Jordan. Explicit second-order min-max optimization methods with optimal convergence guarantees.April 2024HALback to text
• 41 miscI.Iosif Lytras and P.Panayotis Mertikopoulos. Tamed Langevin sampling under weaker conditions.May 2024HALback to text
• 42 miscM.Mark Turner, T.Timo Berthold, M.Mathieu Besançon and T.Thorsten Koch. Branching via Cutting Plane Selection: Improving Hybrid Branching.February 2024HALback to text