Search Results for author: Panayotis Mertikopoulos

Found 59 papers, 0 papers with code

Gradient-free Online Learning in Continuous Games with Delayed Rewards

no code implementations ICML 2020 Amélie Héliou, Panayotis Mertikopoulos, Zhengyuan Zhou

Motivated by applications to online advertising and recommender systems, we consider a game-theoretic model with delayed rewards and asynchronous, payoff-based feedback.

Multi-Armed Bandits online learning +1

On the rate of convergence of Bregman proximal methods in constrained variational inequalities

no code implementations15 Nov 2022 Waïss Azizian, Franck Iutzeler, Jérôme Malick, Panayotis Mertikopoulos

We examine the last-iterate convergence rate of Bregman proximal methods - from mirror descent to mirror-prox - in constrained variational inequalities.

Explicit Second-Order Min-Max Optimization Methods with Optimal Convergence Guarantee

no code implementations23 Oct 2022 Tianyi Lin, Panayotis Mertikopoulos, Michael I. Jordan

We propose and analyze exact and inexact regularized Newton-type methods for finding a global saddle point of a \textit{convex-concave} unconstrained min-max optimization problem.

Second-order methods

On the convergence of policy gradient methods to Nash equilibria in general stochastic games

no code implementations17 Oct 2022 Angeliki Giannou, Kyriakos Lotidis, Panayotis Mertikopoulos, Emmanouil-Vasileios Vlatakis-Gkaragkounis

Learning in stochastic games is a notoriously difficult problem because, in addition to each other's strategic decisions, the players must also contend with the fact that the game itself evolves over time, possibly in a very complicated manner.

Policy Gradient Methods

Pick your Neighbor: Local Gauss-Southwell Rule for Fast Asynchronous Decentralized Optimization

no code implementations15 Jul 2022 Marina Costantini, Nikolaos Liakopoulos, Panayotis Mertikopoulos, Thrasyvoulos Spyropoulos

In decentralized optimization environments, each agent $i$ in a network of $n$ nodes has its own private function $f_i$, and nodes communicate with their neighbors to cooperatively minimize the aggregate objective $\sum_{i=1}^n f_i$.

Nested bandits

no code implementations19 Jun 2022 Matthieu Martin, Panayotis Mertikopoulos, Thibaud Rahier, Houssam Zenati

In many online decision processes, the optimizing agent is called to choose between large numbers of alternatives with many inherent similarities; in turn, these similarities imply closely correlated losses that may confound standard discrete choice models and bandit algorithms.

online learning

The Dynamics of Riemannian Robbins-Monro Algorithms

no code implementations14 Jun 2022 Mohammad Reza Karimi, Ya-Ping Hsieh, Panayotis Mertikopoulos, Andreas Krause

Many important learning algorithms, such as stochastic gradient methods, are often deployed to solve nonlinear problems on Riemannian manifolds.

No-Regret Learning in Games with Noisy Feedback: Faster Rates and Adaptivity via Learning Rate Separation

no code implementations13 Jun 2022 Yu-Guan Hsieh, Kimon Antonakopoulos, Volkan Cevher, Panayotis Mertikopoulos

We examine the problem of regret minimization when the learner is involved in a continuous game with other optimizing agents: in this case, if all players follow a no-regret algorithm, it is possible to achieve significantly lower regret relative to fully adversarial environments.

Learning in games from a stochastic approximation viewpoint

no code implementations8 Jun 2022 Panayotis Mertikopoulos, Ya-Ping Hsieh, Volkan Cevher

We develop a unified stochastic approximation framework for analyzing the long-run behavior of multi-agent online learning in games.

online learning

Fast Routing under Uncertainty: Adaptive Learning in Congestion Games via Exponential Weights

no code implementations NeurIPS 2021 Dong Quan Vu, Kimon Antonakopoulos, Panayotis Mertikopoulos

We examine an adaptive learning framework for nonatomic congestion games where the players' cost functions may be subject to exogenous fluctuations (e. g., due to disturbances in the network, variations in the traffic going through a link).

Sifting through the noise: Universal first-order methods for stochastic variational inequalities

no code implementations NeurIPS 2021 Kimon Antonakopoulos, Thomas Pethick, Ali Kavis, Panayotis Mertikopoulos, Volkan Cevher

Our first result is that the algorithm achieves the optimal rates of convergence for cocoercive problems when the profile of the randomness is known to the optimizer: $\mathcal{O}(1/\sqrt{T})$ for absolute noise profiles, and $\mathcal{O}(1/T)$ for relative ones.

Zeroth-order non-convex learning via hierarchical dual averaging

no code implementations13 Sep 2021 Amélie Héliou, Matthieu Martin, Panayotis Mertikopoulos, Thibaud Rahier

We propose a hierarchical version of dual averaging for zeroth-order online non-convex optimization - i. e., learning processes where, at each stage, the optimizer is facing an unknown non-convex loss function and only receives the incurred loss as feedback.

Adaptive first-order methods revisited: Convex optimization without Lipschitz requirements

no code implementations NeurIPS 2021 Kimon Antonakopoulos, Panayotis Mertikopoulos

We propose a new family of adaptive first-order methods for a class of convex minimization problems that may fail to be Lipschitz continuous or smooth in the standard sense.

Distributed stochastic optimization with large delays

no code implementations6 Jul 2021 Zhengyuan Zhou, Panayotis Mertikopoulos, Nicholas Bambos, Peter W. Glynn, Yinyu Ye

One of the most widely used methods for solving large-scale stochastic optimization problems is distributed asynchronous stochastic gradient descent (DASGD), a family of algorithms that result from parallelizing stochastic gradient descent on distributed computing architectures (possibly) asychronously.

Distributed Computing Stochastic Optimization

The Last-Iterate Convergence Rate of Optimistic Mirror Descent in Stochastic Variational Inequalities

no code implementations5 Jul 2021 Waïss Azizian, Franck Iutzeler, Jérôme Malick, Panayotis Mertikopoulos

In this paper, we analyze the local convergence rate of optimistic mirror descent methods in stochastic variational inequalities, a class of optimization problems with important applications to learning theory and machine learning.

Learning Theory

Learning in nonatomic games, Part I: Finite action spaces and population games

no code implementations4 Jul 2021 Saeed Hadikhanloo, Rida Laraki, Panayotis Mertikopoulos, Sylvain Sorin

We examine the long-run behavior of a wide range of dynamics for learning in nonatomic games, in both discrete and continuous time.

Optimization in Open Networks via Dual Averaging

no code implementations27 May 2021 Yu-Guan Hsieh, Franck Iutzeler, Jérôme Malick, Panayotis Mertikopoulos

In networks of autonomous agents (e. g., fleets of vehicles, scattered sensors), the problem of minimizing the sum of the agents' local functions has received a lot of interest.

Distributed Optimization

Adaptive First-Order Methods Revisited: Convex Minimization without Lipschitz Requirements

no code implementations NeurIPS 2021 Kimon Antonakopoulos, Panayotis Mertikopoulos

We propose a new family of adaptive first-order methods for a class of convex minimization problems that may fail to be Lipschitz continuous or smooth in the standard sense.

Adaptive Learning in Continuous Games: Optimal Regret Bounds and Convergence to Nash Equilibrium

no code implementations26 Apr 2021 Yu-Guan Hsieh, Kimon Antonakopoulos, Panayotis Mertikopoulos

In game-theoretic learning, several agents are simultaneously following their individual interests, so the environment is non-stationary from each player's perspective.

Survival of the strictest: Stable and unstable equilibria under regularized learning with partial information

no code implementations12 Jan 2021 Angeliki Giannou, Emmanouil-Vasileios Vlatakis-Gkaragkounis, Panayotis Mertikopoulos

This equivalence extends existing continuous-time versions of the folk theorem of evolutionary game theory to a bona fide algorithmic learning setting, and it provides a clear refinement criterion for the prediction of the day-to-day behavior of no-regret learning in games

Multi-Armed Bandits

Multi-Agent Online Optimization with Delays: Asynchronicity, Adaptivity, and Optimism

no code implementations21 Dec 2020 Yu-Guan Hsieh, Franck Iutzeler, Jérôme Malick, Panayotis Mertikopoulos

In this paper, we provide a general framework for studying multi-agent online learning problems in the presence of delays and asynchronicities.

online learning

Adaptive extra-gradient methods for min-max optimization and games

no code implementations ICLR 2021 Kimon Antonakopoulos, E. Veronica Belmega, Panayotis Mertikopoulos

We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones.

Regret minimization in stochastic non-convex learning via a proximal-gradient approach

no code implementations13 Oct 2020 Nadav Hallak, Panayotis Mertikopoulos, Volkan Cevher

In this setting, the minimization of external regret is beyond reach for first-order methods, so we focus on a local regret measure defined via a proximal-gradient mapping.

Stochastic Optimization

On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems

no code implementations NeurIPS 2020 Panayotis Mertikopoulos, Nadav Hallak, Ali Kavis, Volkan Cevher

This paper analyzes the trajectories of stochastic gradient descent (SGD) to help understand the algorithm's convergence properties in non-convex problems.

The limits of min-max optimization algorithms: convergence to spurious non-critical sets

no code implementations16 Jun 2020 Ya-Ping Hsieh, Panayotis Mertikopoulos, Volkan Cevher

Compared to ordinary function minimization problems, min-max optimization algorithms encounter far greater challenges because of the existence of periodic cycles and similar phenomena.

Online and stochastic optimization beyond Lipschitz continuity: A Riemannian approach

no code implementations ICLR 2020 Kimon Antonakopoulos, E. Veronica Belmega, Panayotis Mertikopoulos

Motivated by applications to machine learning and imaging science, we study a class of online and stochastic optimization problems with loss functions that are not Lipschitz continuous; in particular, the loss functions encountered by the optimizer could exhibit gradient singularities or be singular themselves.

Stochastic Optimization

Explore Aggressively, Update Conservatively: Stochastic Extragradient Methods with Variable Stepsize Scaling

no code implementations NeurIPS 2020 Yu-Guan Hsieh, Franck Iutzeler, Jérôme Malick, Panayotis Mertikopoulos

Owing to their stability and convergence speed, extragradient methods have become a staple for solving large-scale saddle-point problems in machine learning.

A new regret analysis for Adam-type algorithms

no code implementations ICML 2020 Ahmet Alacaoglu, Yura Malitsky, Panayotis Mertikopoulos, Volkan Cevher

In this paper, we focus on a theory-practice gap for Adam and its variants (AMSgrad, AdamNC, etc.).

Finite-Time Last-Iterate Convergence for Multi-Agent Learning in Games

no code implementations ICML 2020 Tianyi Lin, Zhengyuan Zhou, Panayotis Mertikopoulos, Michael. I. Jordan

In this paper, we consider multi-agent learning via online gradient descent in a class of games called $\lambda$-cocoercive games, a fairly broad class of games that admits many Nash equilibria and that properly includes unconstrained strongly monotone games.

online learning

An adaptive Mirror-Prox method for variational inequalities with singular operators

no code implementations NeurIPS 2019 Kimon Antonakopoulos, Veronica Belmega, Panayotis Mertikopoulos

Lipschitz continuity is a central requirement for achieving the optimal O(1/T) rate of convergence in monotone, deterministic variational inequalities (a setting that includes convex minimization, convex-concave optimization, nonatomic games, and many other problems).

On the convergence of single-call stochastic extra-gradient methods

no code implementations NeurIPS 2019 Yu-Guan Hsieh, Franck Iutzeler, Jérôme Malick, Panayotis Mertikopoulos

Variational inequalities have recently attracted considerable interest in machine learning as a flexible paradigm for models that go beyond ordinary loss function minimization (such as generative adversarial networks and related deep learning systems).

Optimistic mirror descent in saddle-point problems: Going the extra(-gradient) mile

no code implementations ICLR 2019 Panayotis Mertikopoulos, Bruno Lecouat, Houssam Zenati, Chuan-Sheng Foo, Vijay Chandrasekhar, Georgios Piliouras

Owing to their connection with generative adversarial networks (GANs), saddle-point problems have recently attracted considerable interest in machine learning and beyond.

Forward-backward-forward methods with variance reduction for stochastic variational inequalities

no code implementations9 Feb 2019 Radu Ioan Bot, Panayotis Mertikopoulos, Mathias Staudigl, Phan Tu Vuong

We develop a new stochastic algorithm with variance reduction for solving pseudo-monotone stochastic variational inequalities.

Bandit Learning in Concave N-Person Games

no code implementations NeurIPS 2018 Mario Bravo, David Leslie, Panayotis Mertikopoulos

This paper examines the long-run behavior of learning with bandit feedback in non-cooperative concave games.

Stochastic Optimization

Learning in Games with Lossy Feedback

no code implementations NeurIPS 2018 Zhengyuan Zhou, Panayotis Mertikopoulos, Susan Athey, Nicholas Bambos, Peter W. Glynn, Yinyu Ye

We consider a game-theoretical multi-agent learning problem where the feedback information can be lost during the learning process and rewards are given by a broad class of games known as variationally stable games.

online learning

Bandit learning in concave $N$-person games

no code implementations3 Oct 2018 Mario Bravo, David S. Leslie, Panayotis Mertikopoulos

This paper examines the long-run behavior of learning with bandit feedback in non-cooperative concave games.

Stochastic Optimization

Hessian barrier algorithms for linearly constrained optimization problems

no code implementations25 Sep 2018 Immanuel M. Bomze, Panayotis Mertikopoulos, Werner Schachinger, Mathias Staudigl

In the case of linearly constrained quadratic programs (not necessarily convex), we also show that the method's convergence rate is $\mathcal{O}(1/k^\rho)$ for some $\rho\in(0, 1]$ that depends only on the choice of kernel function (i. e., not on the problem's primitives).

Multi-agent online learning in time-varying games

no code implementations10 Sep 2018 Benoit Duvocelle, Panayotis Mertikopoulos, Mathias Staudigl, Dries Vermeulen

We examine the long-run behavior of multi-agent online learning in games that evolve over time.

online learning

Optimistic mirror descent in saddle-point problems: Going the extra (gradient) mile

no code implementations7 Jul 2018 Panayotis Mertikopoulos, Bruno Lecouat, Houssam Zenati, Chuan-Sheng Foo, Vijay Chandrasekhar, Georgios Piliouras

Owing to their connection with generative adversarial networks (GANs), saddle-point problems have recently attracted considerable interest in machine learning and beyond.

Distributed Asynchronous Optimization with Unbounded Delays: How Slow Can You Go?

no code implementations ICML 2018 Zhengyuan Zhou, Panayotis Mertikopoulos, Nicholas Bambos, Peter Glynn, Yinyu Ye, Li-Jia Li, Li Fei-Fei

One of the most widely used optimization methods for large-scale machine learning problems is distributed asynchronous stochastic gradient descent (DASGD).

Online convex optimization and no-regret learning: Algorithms, guarantees and applications

no code implementations12 Apr 2018 E. Veronica Belmega, Panayotis Mertikopoulos, Romain Negrel, Luca Sanguinetti

Spurred by the enthusiasm surrounding the "Big Data" paradigm, the mathematical and algorithmic tools of online optimization have found widespread use in problems where the trade-off between data exploration and exploitation plays a predominant role.

Metric Learning

Learning with Bandit Feedback in Potential Games

no code implementations NeurIPS 2017 Amélie Heliou, Johanne Cohen, Panayotis Mertikopoulos

This paper examines the equilibrium convergence properties of no-regret learning with exponential weights in potential games.

Stochastic Mirror Descent in Variationally Coherent Optimization Problems

no code implementations NeurIPS 2017 Zhengyuan Zhou, Panayotis Mertikopoulos, Nicholas Bambos, Stephen Boyd, Peter W. Glynn

In this paper, we examine a class of non-convex stochastic optimization problems which we call variationally coherent, and which properly includes pseudo-/quasiconvex and star-convex optimization problems.

Stochastic Optimization

Countering Feedback Delays in Multi-Agent Learning

no code implementations NeurIPS 2017 Zhengyuan Zhou, Panayotis Mertikopoulos, Nicholas Bambos, Peter W. Glynn, Claire Tomlin

We consider a model of game-theoretic learning based on online mirror descent (OMD) with asynchronous and delayed feedback information.

Cycles in adversarial regularized learning

no code implementations8 Sep 2017 Panayotis Mertikopoulos, Christos Papadimitriou, Georgios Piliouras

Regularized learning is a fundamental technique in online optimization, machine learning and many other fields of computer science.

On the convergence of mirror descent beyond stochastic convex programming

no code implementations18 Jun 2017 Zhengyuan Zhou, Panayotis Mertikopoulos, Nicholas Bambos, Stephen Boyd, Peter Glynn

In this paper, we examine the convergence of mirror descent in a class of stochastic optimization problems that are not necessarily convex (or even quasi-convex), and which we call variationally coherent.

Stochastic Optimization

On the convergence of gradient-like flows with noisy gradient input

no code implementations21 Nov 2016 Panayotis Mertikopoulos, Mathias Staudigl

In the vanishing noise limit, we show that the dynamics converge to the solution set of the underlying problem (a. s.).

Learning in games with continuous action sets and unknown payoff functions

no code implementations25 Aug 2016 Panayotis Mertikopoulos, Zhengyuan Zhou

This paper examines the convergence of no-regret learning in games with continuous action sets.

Exponentially fast convergence to (strict) equilibrium via hedging

no code implementations29 Jul 2016 Johanne Cohen, Amélie Héliou, Panayotis Mertikopoulos

Motivated by applications to data networks where fast convergence is essential, we analyze the problem of learning in generic N-person games that admit a Nash equilibrium in pure strategies.

Distributed stochastic optimization via matrix exponential learning

no code implementations3 Jun 2016 Panayotis Mertikopoulos, E. Veronica Belmega, Romain Negrel, Luca Sanguinetti

In this paper, we investigate a distributed learning scheme for a broad class of stochastic optimization problems and games that arise in signal processing and wireless communications.

Stochastic Optimization

Boltzmann meets Nash: Energy-efficient routing in optical networks under uncertainty

no code implementations4 May 2016 Panayotis Mertikopoulos, Aris L. Moustakas, Anna Tzanakaki

Motivated by the massive deployment of power-hungry data centers for service provisioning, we examine the problem of routing in optical networks with the aim of minimizing traffic-driven power consumption.

On the robustness of learning in games with stochastically perturbed payoff observations

no code implementations20 Dec 2014 Mario Bravo, Panayotis Mertikopoulos

Motivated by the scarcity of accurate payoff feedback in practical applications of game theory, we examine a class of learning dynamics where players adjust their choices based on past payoff observations that are subject to noise and random disturbances.

Game-theoretical control with continuous action sets

no code implementations1 Dec 2014 Steven Perkins, Panayotis Mertikopoulos, David S. Leslie

To do so, we extend the theory of finite-dimensional two-timescale stochastic approximation to an infinite-dimensional, Banach space setting, and we prove that the continuous dynamics of the process converge to equilibrium in the case of potential games.

Learning in games via reinforcement and regularization

no code implementations23 Jul 2014 Panayotis Mertikopoulos, William H. Sandholm

We investigate a class of reinforcement learning dynamics where players adjust their strategies based on their actions' cumulative payoffs over time - specifically, by playing mixed strategies that maximize their expected cumulative payoff minus a regularization term.

reinforcement-learning

A continuous-time approach to online optimization

no code implementations27 Jan 2014 Joon Kwon, Panayotis Mertikopoulos

We consider a family of learning strategies for online optimization problems that evolve in continuous time and we show that they lead to no regret.

Penalty-regulated dynamics and robust learning procedures in games

no code implementations9 Mar 2013 Pierre Coucheney, Bruno Gaujal, Panayotis Mertikopoulos

Starting from a heuristic learning scheme for N-person games, we derive a new class of continuous-time learning dynamics consisting of a replicator-like drift adjusted by a penalty term that renders the boundary of the game's strategy space repelling.

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