Decentralized PAC Learning in Turn-Based Stochastic Games

Learning reachability objectives in reinforcement learning, particularly in turn-based stochastic games (TBSGs) with two adversarial players, is inherently challenging. Previous approaches to PAC learning in TBSGs often assumed public information sharing and centralized learning algorithms. This new work significantly relaxes these assumptions. The paper introduces a novel framework that enables learning in TBSGs with reachability objectives under conditions of private information, where players do not share their observations, and decentralized learning, where players utilize distinct learning algorithms. This represents a breakthrough, offering the first positive results for such complex, adversarial, and information-constrained environments. Furthermore, the research defines a game-theoretic extension of the Expected Conditional Distance (ECD) parameter, which quantifies the expected time to reach a target state. It also establishes a polynomial-sample complexity bound, indicating the efficiency of the proposed learning approach relative to key game parameters.