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We propose iterative algorithms to solve adversarial problems in a variety of supervised learning settings of interest. Our algorithms, which can be interpreted as suitable ascent-descent dynamics in Wasserstein spaces, take the form of a…

Game theoretic methods have become popular for planning and prediction in situations involving rich multi-agent interactions. However, these methods often assume the existence of a single local Nash equilibria and are hence unable to handle…

Adversarial formulations such as generative adversarial networks (GANs) have rekindled interest in two-player min-max games. A central obstacle in the optimization of such games is the rotational dynamics that hinder their convergence. In…

We study policy optimization algorithms for computing correlated equilibria in multi-player general-sum Markov Games. Previous results achieve $O(T^{-1/2})$ convergence rate to a correlated equilibrium and an accelerated $O(T^{-3/4})$…

Dynamic games arise when multiple agents with differing objectives choose control inputs to a dynamic system. Dynamic games model a wide variety of applications in economics, defense, and energy systems. However, compared to single-agent…

We present a new method for computation of the index of completely mixed equilibria in finite games, based on the work of Eisenbud et al.(1977). We apply this method to solving two questions about the relation of the index of equilibria and…

In many settings where multiple agents interact, the optimal choices for each agent depend heavily on the choices of the others. These coupled interactions are well-described by a general-sum differential game, in which players have…

Min-max formulations have attracted great attention in the ML community due to the rise of deep generative models and adversarial methods, while understanding the dynamics of gradient algorithms for solving such formulations has remained a…

We analyze the problem of identifying large cliques in graphs that are affected by adversarial uncertainty. More specifically, we consider a new formulation, namely the adversarial maximum clique problem, which extends the classical…

This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a new framework to prove convergence…

Zero-sum games have long guided artificial intelligence research, since they possess both a rich strategy space of best-responses and a clear evaluation metric. What's more, competition is a vital mechanism in many real-world multi-agent…

We formulate and study a general time-varying multi-agent system where players repeatedly compete under incomplete information. Our work is motivated by scenarios commonly observed in online advertising and retail marketplaces, where agents…

Autonomous agents should coordinate effectively without prior knowledge of others' intents. While prior work has focused on intent inference, we address the inverse problem: how agents can strategically demonstrate their intents within…

Whether a PTAS (polynomial-time approximation scheme) exists for game equilibria has been an open question, and its absence has indications and consequences in three fields: the practicality of methods in algorithmic game theory,…

A class of nonzero-sum stochastic dynamic games with imperfect information structure is investigated. The game involves an arbitrary number of players, modeled as homogeneous Markov decision processes, aiming to find a sequential Nash…

In two player bi-matrix games with partial monitoring, actions played are not observed, only some messages are received. Those games satisfy a crucial property of usual bi-matrix games: there are only a finite number of required (mixed)…

An interesting iterative procedure is proposed to solve a two-player zero-sum Markov games. Under suitable assumption, the boundedness of the proposed iterates is obtained theoretically. Using results from stochastic approximation, the…

In this paper we investigate the Follow the Regularized Leader dynamics in sequential imperfect information games (IIG). We generalize existing results of Poincar\'e recurrence from normal-form games to zero-sum two-player imperfect…

Computational equilibrium finding in large zero-sum extensive-form imperfect-information games has led to significant recent AI breakthroughs. The fastest algorithms for the problem are new forms of counterfactual regret minimization [Brown…

In this note, we consider repeated play of a finite game using learning rules whose period-by-period behavior probabilities or empirical distributions converge to some notion of equilibria of the stage game. Our primary focus is on…