2022/03/31 by Yuanhanqing Huang, Huang, Yuanhanqing, Jianghai Hu +1 · 1 citation
Medicine · #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2204.00100
openalex publication_date 2022/03/31 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
In stochastic Nash equilibrium problems (SNEPs), it is natural for players to be uncertain about their complex environments and have multi-dimensional unknown parameters in their models. Among various SNEPs, this paper focuses on locally coupled network games where the objective of each rational player is subject to the aggregate influence of its neighbors. We propose a distributed learning algorithm based on the proximal-point iteration and ordinary least-square estimator, where each player repeatedly updates the local estimates of neighboring decisions, makes its augmented best-response decisions given the current estimated parameters, receives the realized objective values, and learns the unknown parameters. Leveraging the Robbins-Siegmund theorem and the law of large deviations for M-estimators, we establish the almost sure convergence of the proposed algorithm to solutions of SNEPs when the updating step sizes decay at a proper rate.