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Recent applications that arise in machine learning have surged significant interest in solving min-max saddle point games. This problem has been extensively studied in the convex-concave regime for which a global equilibrium solution can be…

No-regret learning dynamics play a central role in game theory, enabling decentralized convergence to equilibrium for concepts such as Coarse Correlated Equilibrium (CCE) or Correlated Equilibrium (CE). In this work, we improve the…

This paper investigates posterior sampling algorithms for competitive reinforcement learning (RL) in the context of general function approximations. Focusing on zero-sum Markov games (MGs) under two critical settings, namely self-play and…

The standard risk minimization paradigm of machine learning is brittle when operating in environments whose test distributions are different from the training distribution due to spurious correlations. Training on data from many…

We use co-evolutionary genetic algorithms to model the players' learning process in several Cournot models, and evaluate them in terms of their convergence to the Nash Equilibrium. The "social-learning" versions of the two co-evolutionary…

Nash equilibria are crucial for understanding game behavior and systems in economics, physics, biology, and computer science. A significant application arises from the connection between Nash equilibria and optimization problems . However,…

Multi-agent Inverse Reinforcement Learning (MAIRL) aims to recover agent reward functions from expert demonstrations. We characterize the feasible reward set in Markov games, identifying all reward functions that rationalize a given…

A recent body of experimental literature has studied empirical game-theoretical analysis, in which we have partial knowledge of a game, consisting of observations of a subset of the pure-strategy profiles and their associated payoffs to…

When solving two-player zero-sum games, multi-agent reinforcement learning (MARL) algorithms often create populations of agents where, at each iteration, a new agent is discovered as the best response to a mixture over the opponent…

We introduce a new algorithm for the numerical computation of Nash equilibria of competitive two-player games. Our method is a natural generalization of gradient descent to the two-player setting where the update is given by the Nash…

Zero-sum games arise in a wide variety of problems, including robust optimization and adversarial learning. However, algorithms deployed for finding a local Nash equilibrium in these games often converge to non-Nash stationary points. This…

We study the problem of computing an $\epsilon$-approximate Nash equilibrium of a two-player, bilinear game with a bounded payoff matrix $A \in \mathbb{R}^{m \times n}$, when the players' strategies are constrained to lie in simple sets. We…

The designs of many large-scale systems today, from traffic routing environments to smart grids, rely on game-theoretic equilibrium concepts. However, as the size of an $N$-player game typically grows exponentially with $N$, standard game…

Multi-agent interactions are increasingly important in the context of reinforcement learning, and the theoretical foundations of policy gradient methods have attracted surging research interest. We investigate the global convergence of…

We reconsider the training objective of Generative Adversarial Networks (GANs) from the mixed Nash Equilibria (NE) perspective. Inspired by the classical prox methods, we develop a novel algorithmic framework for GANs via an…

Designing socially optimal policies in multi-agent environments is a fundamental challenge in both economics and artificial intelligence. This paper studies a general framework for learning Stackelberg equilibria in dynamic and uncertain…

Consider a strongly monotone game where the players' utility functions include a reward function and a linear term for each dimension, with coefficients that are controlled by the manager. Gradient play converges to a unique Nash…

We consider multi-agent decision making, where each agent optimizes its cost function subject to constraints. Agents' actions belong to a compact convex Euclidean space and the agents' cost functions are coupled. We propose a distributed…

Nash equilibrium is perhaps the best-known solution concept in game theory. Such a solution assigns a strategy to each player which offers no incentive to unilaterally deviate. While a Nash equilibrium is guaranteed to always exist, the…

Model-based algorithms -- algorithms that explore the environment through building and utilizing an estimated model -- are widely used in reinforcement learning practice and theoretically shown to achieve optimal sample efficiency for…