On the Use of Non-Stationary Policies for Stationary Infinite-Horizon Markov Decision Processes

Part of Advances in Neural Information Processing Systems 25 (NIPS 2012)

Authors

Bruno Scherrer, Boris Lesner

Abstract

We consider infinite-horizon stationary $\gamma$-discounted Markov Decision Processes, for which it is known that there exists a stationary optimal policy. Using Value and Policy Iteration with some error $\epsilon$ at each iteration, it is well-known that one can compute stationary policies that are $\frac{2\gamma{(1-\gamma)^2}\epsilon$-optimal. After arguing that this guarantee is tight, we develop variations of Value and Policy Iteration for computing non-stationary policies that can be up to$\frac{2\gamma}{1-\gamma}\epsilon$-optimal, which constitutes a significant improvement in the usual situation when$\gamma$is close to$1$. Surprisingly, this shows that the problem of computing near-optimal non-stationary policies'' is much simpler than that of computing near-optimal stationary policies''.