Online Reinforcement Learning via Posterior Sampling of Policy

We propose a Reward-Weighted Posterior Sampling of Policy (RWPSP) algorithm to tackle the classic trade-off problem between exploration and exploitation under finite Markov decision processes (MDPs). The Thompson sampling method so far has only considered posterior sampling over transition probabilities, which is hard to gain the globally sub-optimal rewards. RWPSP runs posterior sampling over stationary policy distributions instead of transition probabilities, and meanwhile keeps transition probabilities updated. Particularly, we leverage both relevant count functions and reward-weighting to online update the policy posterior, aiming to balance between local and long-term policy distributions for a globally near-optimal game value. Theoretically, we establish a bound of $\tilde{\mathcal{O}}(\Gamma\sqrt{T}/S^{2})$\footnote{The symbol $\tilde{\mathcal{O}}$ hides logarithmic factors.} on the total regret in time horizon $T$ with $\Gamma/S^{2} < D\sqrt{SA}$ satisfied in general, where $S$ and $A$ represents the sizes of state and action spaces, respectively, $D$ the diameter. This matches the best regret bound thus far for MDPs. Experimental results corroborate our theoretical results and show the advantage of our algorithm over the state of the art in terms of efficiency.