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

Bruno Scherrer 1 Boris Lesner 1
1 MAIA - Autonomous intelligent machine
Inria Nancy - Grand Est, LORIA - AIS - Department of Complex Systems, Artificial Intelligence & Robotics
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. On the Use of Non-Stationary Policies for Stationary Infinite-Horizon Markov Decision Processes. NIPS 2012 - Neural Information Processing Systems, Dec 2012, South Lake Tahoe, United States. ⟨hal-00758809⟩

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