2022/08/21 by Kenshi Abe, Kaito Ariu, Abe, Kenshi +7 · 3 citations
Decision Sciences · Social Sciences · #Advanced Bandit Algorithms Research #Computer Science and Game Theory (cs.GT) #Experimental Behavioral Economics Studies #FOS: Computer and information sciences #Game Theory and Applications #Machine Learning (cs.LG)
paper · pdf · doi:10.48550/arxiv.2208.09855
openalex publication_date 2022/08/21 · openalex created_date 2022/08/24 · openalex updated_date 2026/07/28
This paper proposes Mutation-Driven Multiplicative Weights Update (M2WU) for learning an equilibrium in two-player zero-sum normal-form games and proves that it exhibits the last-iterate convergence property in both full and noisy feedback settings. In the former, players observe their exact gradient vectors of the utility functions. In the latter, they only observe the noisy gradient vectors. Even the celebrated Multiplicative Weights Update (MWU) and Optimistic MWU (OMWU) algorithms may not converge to a Nash equilibrium with noisy feedback. On the contrary, M2WU exhibits the last-iterate convergence to a stationary point near a Nash equilibrium in both feedback settings. We then prove that it converges to an exact Nash equilibrium by iteratively adapting the mutation term. We empirically confirm that M2WU outperforms MWU and OMWU in exploitability and convergence rates.