Online Monotone Games

TL;DR

This paper introduces the concept of online monotone games, extending game theory to online settings with new algorithms that achieve sub-linear regret, applicable to diverse domains like reinforcement learning and GANs.

Contribution

It defines the online monotone game framework, introduces a new regret notion, and develops algorithms with sub-linear regret guarantees for this setting.

Findings

Established the online monotone game framework.

Designed algorithms with sub-linear regret.

Validated applicability in RL, GANs, and variational inequalities.

Abstract

Algorithmic game theory (AGT) focuses on the design and analysis of algorithms for interacting agents, with interactions rigorously formalized within the framework of games. Results from AGT find applications in domains such as online bidding auctions for web advertisements and network routing protocols. Monotone games are games where agent strategies naturally converge to an equilibrium state. Previous results in AGT have been obtained for convex, socially-convex, or smooth games, but not monotone games. Our primary theoretical contributions are defining the monotone game setting and its extension to the online setting, a new notion of regret for this setting, and accompanying algorithms that achieve sub-linear regret. We demonstrate the utility of online monotone game theory on a variety of problem domains including variational inequalities, reinforcement learning, and generative adversarial networks.