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In this work, we study the sample complexity of obtaining a Nash equilibrium (NE) estimate in two-player zero-sum matrix games with noisy feedback. Specifically, we propose a novel algorithm that repeatedly solves linear programs (LPs) to…

This paper considers the problem of designing optimal algorithms for reinforcement learning in two-player zero-sum games. We focus on self-play algorithms which learn the optimal policy by playing against itself without any direct…

In this paper, we study the problem of learning the exact structure of continuous-action games with non-parametric utility functions. We propose an $\ell_1$ regularized method which encourages sparsity of the coefficients of the Fourier…

Model-free learning for multi-agent stochastic games is an active area of research. Existing reinforcement learning algorithms, however, are often restricted to zero-sum games, and are applicable only in small state-action spaces or other…

We propose efficient no-regret learning dynamics and ellipsoid-based methods for computing linear correlated equilibria$\unicode{x2014}$a relaxation of correlated equilibria and a strengthening of coarse correlated…

Nash equilibrium is a central concept in game theory. Several Nash solvers exist, yet none scale to normal-form games with many actions and many players, especially those with payoff tensors too big to be stored in memory. In this work, we…

This paper explores distributed aggregative games in multi-agent systems. Current methods for finding distributed Nash equilibrium require players to send original messages to their neighbors, leading to communication burden and privacy…

We consider payoff-based learning of a generalized Nash equilibrium (GNE) in multi-agent systems. Our focus is on games with jointly convex constraints of a linear structure and strongly monotone pseudo-gradients. We present a convergent…

In this paper, we propose a numerical methodology for finding the closed-loop Nash equilibrium of stochastic delay differential games through deep learning. These games are prevalent in finance and economics where multi-agent interaction…

We design the first fully-distributed algorithm for generalized Nash equilibrium seeking in aggregative games on a time-varying communication network, under partial-decision information, i.e., the agents have no direct access to the…

Over the years, researchers have studied the complexity of several decision versions of Nash equilibrium in (symmetric) two-player games (bimatrix games). To the best of our knowledge, the last remaining open problem of this sort is the…

The computational study of equilibria involving constraints on players' strategies has been largely neglected. However, in real-world applications, players are usually subject to constraints ruling out the feasibility of some of their…

We design a distributed algorithm for learning Nash equilibria over time-varying communication networks in a partial-decision information scenario, where each agent can access its own cost function and local feasible set, but can only…

Prediction is a well-studied machine learning task, and prediction algorithms are core ingredients in online products and services. Despite their centrality in the competition between online companies who offer prediction-based products,…

Motivated by the sequence form formulation of Koller et al. (GEB'96), this paper defines {\em bilinear games}, and proposes efficient algorithms for its rank based subclasses. Bilinear games are two-player non-cooperative single-shot games…

In this tutorial, we provide an introduction to machine learning methods for finding Nash equilibria in games with large number of agents. These types of problems are important for the operations research community because of their…

The solution to a Nash or a nonsymmetric bargaining game is obtained by maximizing a concave function over a convex set, i.e., it is the solution to a convex program. We show that each 2-player game whose convex program has linear…

We explore the use of policy approximations to reduce the computational cost of learning Nash equilibria in zero-sum stochastic games. We propose a new Q-learning type algorithm that uses a sequence of entropy-regularized soft policies to…

Nash equilibrium has long been a desired solution concept in multi-player games, especially for those on continuous strategy spaces, which have attracted a rapidly growing amount of interests due to advances in research applications such as…

In 1975 the first author proved that every finite tight two-person game form $g$ is Nash-solvable, that is, for every payoffs $u$ and $w$ of two players the obtained game $(g;u,w)$, in normal form, has a Nash equilibrium (NE) in pure…