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Last iterate convergence in network zero-sum games

University of British Columbia

Motivated by Generative Adverserial Networks, we study the computation of a Nash equilibrium in concave network zero-sum games (NZSGs), a multiplayer generalization of two-player zero-sum games first proposed with linear payoffs. Extending previous results, we show that various game theoretic properties of convex-concave two-player zero-sum games are preserved in this generalization. We then generalize last iterate convergence results obtained previously in two-player zero-sum games. We analyze convergence rates when players update their strategies using Mirror Descent, and Optimistic Mirror Descent. We analyze these algorithms when they are used with the squared l2 norm as a regularizer --- yielding Gradient Ascent, Extra-Gradient Method, and Optimistic Gradient Ascent. We show exponential convergence when the payoffs of players are linear, or strongly concave and smooth. For the more general method of Optimistic Mirror Descent, we show last iterate convergence for any monotone game with bounded gradients, as well as monotonic convergence in games with strictly monotone and smooth payoffs.

Text

2021-01-11

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/77049

Computer Science

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/