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arXiv · 1211.6898

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

Bruno Scherrer·Boris Lesner
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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".

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Bruno Scherrer, Boris Lesner. 2012-11-29. On the Use of Non-Stationary Policies for Stationary Infinite-Horizon Markov Decision Processes. https://arxiv.org/abs/1211.6898

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