Fast Convergence of Optimistic Gradient Ascent in Network Zero-Sum Extensive Form Games

Ryann Sim, EFSTRATIOS PANTELEIMON SKOULAKIS, Lillian J Ratliff, Georgios Piliouras

Keywords: extensive form games, network extensive form games, online learning, optimistic gradient descent ascent

Abstract: 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 (EFG) and particularly in EFGs with many agents lags far behind, despite them being closer in nature to many real world applications. We consider the natural class of Network Zero-Sum Extensive Form Games, which combines the global zero-sum property of agent payoffs, the efficient representation of graphical games as well the expressive power of EFGs. We examine the convergence properties of Optimistic Gradient Ascent (OGA) in these games. We prove that the time-average behavior of such online learning dynamics exhibits $O(1/T)$ rate of convergence to the set of Nash equilibria. Moreover, we show that the day-to-day behavior also converges to Nash with rate $O(c^{-t})$ for some game-dependent constant $c > 0$.

One-sentence Summary: We provide a formulation of network zero-sum extensive form games and show that optimistic gradient ascent admits fast convergence to Nash, both in time average and in the day-to-day sense.