Q-Learning Design for Discrete-Time Stochastic Zero-Sum Games

This study explores the application of the model-free Q-Learning algorithm in discrete-time linear quadratic stochastic zero-sum games. The main contribution is two-fold: firstly, extending the zero-sum game concept to stochastic situation and resolving it through a model-based approach; secondly, introducing a model-free Q-Learning algorithm as an innovative method, differing from conventional policy iteration and value iteration. Detailed mathematical demonstrations are included, validating the model-free Q-Learning algorithm's convergence within this research. A numerical example is provided to demonstrate the algorithm's effectiveness.