Last-Iterate Convergence with Full and Noisy Feedback in Two-Player Zero-Sum Games
This addresses convergence issues in game theory for scenarios with imperfect information, offering a robust solution but is incremental as it builds on existing MWU methods.
The paper tackles the problem of learning equilibria in two-player zero-sum games with full and noisy feedback, proposing M2WU, which achieves last-iterate convergence to a Nash equilibrium, outperforming MWU and OMWU in exploitability and convergence rates.
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.