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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…
Motivated by applications in Optimization, Game Theory, and the training of Generative Adversarial Networks, the convergence properties of first order methods in min-max problems have received extensive study. It has been recognized that…
In this paper we consider solving saddle point problems using two variants of Gradient Descent-Ascent algorithms, Extra-gradient (EG) and Optimistic Gradient Descent Ascent (OGDA) methods. We show that both of these algorithms admit a…
We consider differentiable games where the goal is to find a Nash equilibrium. The machine learning community has recently started using variants of the gradient method (GD). Prime examples are extragradient (EG), the optimistic gradient…
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…
Feedback delays are inevitable in real-world multi-agent learning. They are known to severely degrade performance, and the convergence rate under delayed feedback is still unclear, even for bilinear games. This paper derives the rate of…
Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium…
Zero-sum stochastic games are easy to solve as they can be cast as simple Markov decision processes. This is however not the case with general-sum stochastic games. A fairly general optimization problem formulation is available for…
This paper presents algorithms for non-zero sum nonlinear constrained dynamic games with full information. Such problems emerge when multiple players with action constraints and differing objectives interact with the same dynamic system.…
This paper introduces alignment games, a new class of zero-sum games modeling strategic interventions where effectiveness depends on alignment with an underlying hidden state. Motivated by operational problems in medical diagnostics,…
Finding equilibria via gradient play in competitive multi-agent games has been attracting a growing amount of attention in recent years, with emphasis on designing efficient strategies where the agents operate in a decentralized and…
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…
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…
In order to find Nash-equilibria for two-player zero-sum games where each player plays combinatorial objects like spanning trees, matchings etc, we consider two online learning algorithms: the online mirror descent (OMD) algorithm and the…
Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets, and other areas, but the difficulty in solving such problems has…
Smooth minimax games often proceed by simultaneous or alternating gradient updates. Although algorithms with alternating updates are commonly used in practice, the majority of existing theoretical analyses focus on simultaneous algorithms…
We revisit the problem of solving two-player zero-sum games in the decentralized setting. We propose a simple algorithmic framework that simultaneously achieves the best rates for honest regret as well as adversarial regret, and in addition…
We develop provably efficient reinforcement learning algorithms for two-player zero-sum finite-horizon Markov games with simultaneous moves. To incorporate function approximation, we consider a family of Markov games where the reward…
The study of learning in games has thus far focused primarily on normal form games. In contrast, our understanding of learning in extensive form games (EFGs) and particularly in EFGs with many agents lags far behind, despite them being…
Motivated by Generative Adversarial Networks, we study the computation of Nash equilibrium in concave network zero-sum games (NZSGs), a multiplayer generalization of two-player zero-sum games first proposed with linear payoffs. Extending…