Offline Learning of Decision Functions in Multiplayer Games with Expectation Constraints

• DOI: 10.48550/arxiv.2402.15724
• Publication Date: 2024-01-01
• Authors: Huang, Yuanhanqing; Hu, Jianghai
• Keywords: Optimization and Control (math.OC); FOS: Mathematics; FOS: Electrical engineering, electronic engineering, information engineering; Systems and Control (eess.SY); Mathematics - Optimization and Control; Electrical Engineering and Systems Science - Systems and Control

We explore a class of stochastic multiplayer games where each player in the game aims to optimize its objective under uncertainty and adheres to some expectation constraints. The study employs an offline learning paradigm, leveraging a pre-existing dataset containing auxiliary features. While prior research in deterministic and stochastic multiplayer games primarily explored vector-valued decisions, this work departs by considering function-valued decisions that incorporate auxiliary features as input. We leverage the law of large deviations and degree theory to establish the almost sure convergence of the offline learning solution to the true solution as the number of data samples increases. Finally, we demonstrate the validity of our method via a multi-account portfolio optimization problem.