Related papers: Optimistic Gradient Descent Ascent in Zero-Sum and…

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…

In this paper we present optimization problems with biconvex objective function and linear constraints such that the set of global minima of the optimization problems is the same as the set of Nash equilibria of a n-player general-sum…

We address the issue of limit cycling behavior in training Generative Adversarial Networks and propose the use of Optimistic Mirror Decent (OMD) for training Wasserstein GANs. Recent theoretical results have shown that optimistic mirror…

In a recent series of papers it has been established that variants of Gradient Descent/Ascent and Mirror Descent exhibit last iterate convergence in convex-concave zero-sum games. Specifically, \cite{DISZ17, LiangS18} show last iterate…

Smooth minimax optimization problems play a central role in a wide range of applications, including machine learning, game theory, and operations research. However, existing algorithmic frameworks vary significantly depending on the problem…

We study online optimization methods for zero-sum games, a fundamental problem in adversarial learning in machine learning, economics, and many other domains. Traditional methods approximate Nash equilibria (NE) using either regret-based…

We present a method of backward induction for computing approximate subgame perfect Nash equilibria of infinitely repeated games with discounted payoffs. This uses the selection monad transformer, combined with the searchable set monad…

Despite the established convergence theory of Optimistic Gradient Descent Ascent (OGDA) and Extragradient (EG) methods for the convex-concave minimax problems, little is known about the theoretical guarantees of these methods in nonconvex…

Gradient Descent Ascent (GDA) methods are the mainstream algorithms for minimax optimization in generative adversarial networks (GANs). Convergence properties of GDA have drawn significant interest in the recent literature. Specifically,…

We consider a class of fully stochastic and fully distributed algorithms, that we prove to learn equilibria in games. Indeed, we consider a family of stochastic distributed dynamics that we prove to converge weakly (in the sense of weak…

The approximation of mixed Nash equilibria (MNE) for zero-sum games with mean-field interacting players has recently raised much interest in machine learning. In this paper we propose a mean-field gradient descent dynamics for finding the…

In this work, we introduce the concept of non-negative weighted regret, an extension of non-negative regret \cite{anagnostides2022last} in games. Investigating games with non-negative weighted regret helps us to understand games with…

We generalize gradient descent with momentum for optimization in differentiable games to have complex-valued momentum. We give theoretical motivation for our method by proving convergence on bilinear zero-sum games for simultaneous and…

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…

Wide machine learning tasks can be formulated as non-convex multi-player games, where Nash equilibrium (NE) is an acceptable solution to all players, since no one can benefit from changing its strategy unilaterally. Attributed to the…

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. Specifically, we consider a scenario where…

Many economic games and machine learning approaches can be cast as competitive optimization problems where multiple agents are minimizing their respective objective function, which depends on all agents' actions. While gradient descent is a…

Stochastic min-max optimization has gained interest in the machine learning community with the advancements in GANs and adversarial training. Although game optimization is fairly well understood in the deterministic setting, some issues…

In this paper, we consider two-player zero-sum matrix and stochastic games and develop learning dynamics that are payoff-based, convergent, rational, and symmetric between the two players. Specifically, the learning dynamics for matrix…

Long studied as a toy model, quantum zero-sum games have recently resurfaced as a canonical playground for modern areas such as non-local games, quantum interactive proofs, and quantum machine learning. In this simple yet fundamental…