Forward Looking Best-Response Multiplicative Weights Update Methods

06/07/2021
by   Michail Fasoulakis, et al.
0

We propose a novel variant of the multiplicative weights update method with forward-looking best-response strategies, that guarantees last-iterate convergence for zero-sum games with a unique Nash equilibrium. Particularly, we show that the proposed algorithm converges to an η^1/ρ-approximate Nash equilibrium, with ρ > 1, by decreasing the Kullback-Leibler divergence of each iterate by a rate of at least Ω(η^1+1/ρ), for sufficiently small learning rate η. 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 <cit.>, 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.

READ FULL TEXT
04/25/2022

A dynamic that evolves toward a Nash equilibrium

In this paper, we study an exponentiated multiplicative weights dynamic ...
08/21/2022

Last-Iterate Convergence with Full- and Noisy-Information Feedback in Two-Player Zero-Sum Games

The theory of learning in games is prominent in the AI community, motiva...
01/26/2022

An Efficient Approximation Algorithm for the Colonel Blotto Game

In the storied Colonel Blotto game, two colonels allocate a and b troops...
10/08/2021

Nash Convergence of Mean-Based Learning Algorithms in First Price Auctions

Understanding the convergence properties of learning dynamics in repeate...
06/06/2019

Robust Attacks against Multiple Classifiers

We address the challenge of designing optimal adversarial noise algorith...
06/19/2022

The Power of Regularization in Solving Extensive-Form Games

In this paper, we investigate the power of regularization, a common tech...
06/30/2021

On the Convergence of Stochastic Extragradient for Bilinear Games with Restarted Iteration Averaging

We study the stochastic bilinear minimax optimization problem, presentin...