Forward Looking Best-Response Multiplicative Weights Update Methods

• URL: http://arxiv.org/abs/2106.03579v1
• Date: Mon, 7 Jun 2021 13:03:33 GMT
• Title: Forward Looking Best-Response Multiplicative Weights Update Methods
• Authors: Michail Fasoulakis, Evangelos Markakis, Yannis Pantazis, Constantinos Varsos
• Abstract summary: A novel variant of the emphmultiplicative weights update method guarantees last-iterate convergence for emphzero-sum games with a unique emphNash equilibrium Our findings reveal that our algorithm offers substantial gains both in terms of the convergence rate and the region of contraction relative to the previous approach.
• Score: 14.519198115835966
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a novel variant of the \emph{multiplicative weights update method} with forward-looking best-response strategies, that guarantees last-iterate convergence for \emph{zero-sum games} with a unique \emph{Nash equilibrium}. Particularly, we show that the proposed algorithm converges to an $\eta^{1/\rho}$-approximate Nash equilibrium, with $\rho > 1$, by decreasing the Kullback-Leibler divergence of each iterate by a rate of at least $\Omega(\eta^{1+\frac{1}{\rho}})$, for sufficiently small learning rate $\eta$. When our method enters a sufficiently small neighborhood of the solution, it becomes a contraction and converges to the Nash equilibrium of the game. Furthermore, we perform an experimental comparison with the recently proposed optimistic variant of the multiplicative weights update method, by \cite{Daskalakis2019LastIterateCZ}, which has also been proved to attain last-iterate convergence. Our findings reveal that our algorithm offers substantial gains both in terms of the convergence rate and the region of contraction relative to the previous approach.

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