Bayesian Q-learning with Assumed Density Filtering

While off-policy temporal difference methods have been broadly used in reinforcement learning due to their efficiency and simple implementation, their Bayesian counterparts have been relatively understudied. This is mainly because the max operator in the Bellman optimality equation brings non-linearity and inconsistent distributions over value function. In this paper, we introduce a new Bayesian approach to off-policy TD methods using Assumed Density Filtering, called ADFQ, which updates beliefs on action-values (Q) through an online Bayesian inference method. Uncertainty measures in the beliefs not only are used in exploration but they provide a natural regularization in the belief updates. We also present a connection between ADFQ and Q-learning. Our empirical results show the proposed ADFQ algorithms outperform comparing algorithms in several task domains. Moreover, our algorithms improve general drawbacks in BRL such as computational complexity, usage of uncertainty, and nonlinearity.