A Bayesian reinforcement learning approach in markov games for computing near-optimal policies

Bayesian Learning is an inference method designed to tackle exploration-exploitation trade-off as a function of the uncertainty of a given probability model from observations within the Reinforcement Learning (RL) paradigm. It allows the incorporation of prior knowledge, as probabilistic distributions, into the algorithms. Finding the resulting Bayes-optimal policies is notorious problem. We focus our attention on RL of a special kind of ergodic and controllable Markov games. We propose a new framework for computing the near-optimal policies for each agent, where it is assumed that the Markov chains are regular and the inverse of the behavior strategy is well defined. A fundamental result of this paper is the development of a theoretical method that, based on the formulation of a non-linear problem, computes the near-optimal adaptive-behavior strategies and policies of the game under some restrictions that maximize the expected reward. We prove that such behavior strategies and the policies satisfy the Bayesian-Nash equilibrium. Another important result is that the RL process learn a model through the interaction of the agents with the environment, and shows how the proposed method can finitely approximate and estimate the elements of the transition matrices and utilities maintaining an efficient long-term learning performance measure. We develop the algorithm for implementing this model. A numerical empirical example shows how to deploy the estimation process as a function of agent experiences.