Last-iterate Convergence Separation between Extra-gradient and Optimism in Constrained Periodic Games

Yi Feng, Ping Li, Ioannis Panageas, Xiao Wang

Keywords: last-iterate convergence, time-varying games, optimistic methods, extra-gradient methods

TL;DR: We prove that extra-gradient MWU converges, while optimistic MWU diverges in constrained periodic games.

Abstract: Last-iterate behaviors of learning algorithms in repeated two-player zero-sum games have been extensively studied due to their wide applications in machine learning and related tasks. Typical algorithms that exhibit the last-iterate convergence property include optimistic and extra-gradient methods. However, most existing results establish these properties under the assumption that the game is time-independent. Recently, (Feng et al., 2023) studied the last-iterate behaviors of optimistic and extra-gradient methods in games with a time-varying payoff matrix, and proved that in an unconstrained periodic game, extra-gradient method converges to the equilibrium while optimistic method diverges. This finding challenges the conventional wisdom that these two methods are expected to behave similarly as they do in time-independent games. However, compared to unconstrained games, games with constrains are more common both in practical and theoretical studies. In this paper, we investigate the last-iterate behaviors of optimistic and extra-gradient methods in the constrained periodic games, demonstrating that similar separation results for last-iterate convergence also hold in this setting.

List Of Authors: Yi,Feng and Ping,Li and Ioannis,Panageas and Xiao,Wang

Submission Number: 380