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

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".

References in corpus (1)

• Planning in POMDPs Using Multiplicity Automata

Cited by in corpus (2)

• Approximate Policy Iteration Schemes: A Comparison
• Rate of Convergence and Error Bounds for LSTD($\lambda$)