相关论文: Optimistic Gradient Descent Ascent in Zero-Sum and…

In this work, we establish near-linear and strong convergence for a natural first-order iterative algorithm that simulates Von Neumann's Alternating Projections method in zero-sum games. First, we provide a precise analysis of Optimistic…

We study the alternating gradient descent-ascent (AltGDA) algorithm in two-player zero-sum games. Alternating methods, where players take turns to update their strategies, have long been recognized as simple and practical approaches for…

Self-play via online learning is one of the premier ways to solve large-scale two-player zero-sum games, both in theory and practice. Particularly popular algorithms include optimistic multiplicative weights update (OMWU) and optimistic…

We focus on the design of algorithms for finding equilibria in 2-player zero-sum games. Although it is well known that such problems can be solved by a single linear program, there has been a surge of interest in recent years for simpler…

Optimistic Gradient Descent Ascent (OGDA) and Optimistic Multiplicative Weights Update (OMWU) for saddle-point optimization have received growing attention due to their favorable last-iterate convergence. However, their behaviors for simple…

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…

Last-iterate convergence has received extensive study in two player zero-sum games starting from bilinear, convex-concave up to settings that satisfy the MVI condition. Typical methods that exhibit last-iterate convergence for the…

In this work, we establish a frequency-domain framework for analyzing gradient-based algorithms in linear minimax optimization problems; specifically, our approach is based on the Z-transform, a powerful tool applied in Control Theory and…

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…

Most of the literature on learning in games has focused on the restrictive setting where the underlying repeated game does not change over time. Much less is known about the convergence of no-regret learning algorithms in dynamic multiagent…

We show that, for any sufficiently small fixed $\epsilon > 0$, when both players in a general-sum two-player (bimatrix) game employ optimistic mirror descent (OMD) with smooth regularization, learning rate $\eta = O(\epsilon^2)$ and $T =…

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…

We introduce a generalization of zero-sum network multiagent matrix games and prove that alternating gradient descent converges to the set of Nash equilibria at rate $O(1/T)$ for this set of games. Alternating gradient descent obtains this…

The two-timescale gradient descent-ascent (GDA) is a canonical gradient algorithm designed to find Nash equilibria in min-max games. We analyze the two-timescale GDA by investigating the effects of learning rate ratios on convergence…

Many recent AI architectures are inspired by zero-sum games, however, the behavior of their dynamics is still not well understood. Inspired by this, we study standard gradient descent ascent (GDA) dynamics in a specific class of non-convex…

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…

Motivated by applications in Game Theory, Optimization, and Generative Adversarial Networks, recent work of Daskalakis et al \cite{DISZ17} and follow-up work of Liang and Stokes \cite{LiangS18} have established that a variant of the widely…

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…

Motivated by the pursuit of a systematic computational and algorithmic understanding of Generative Adversarial Networks (GANs), we present a simple yet unified non-asymptotic local convergence theory for smooth two-player games, which…

Min-max optimization problems (i.e., min-max games) have attracted a great deal of attention recently as their applicability to a wide range of machine learning problems has become evident. In this paper, we study min-max games with…