On the Use of Non-Stationary Policies for Stationary Infinite-Horizon Markov Decision Processes
Bruno Scherrer, Boris Lesner · arXiv (Cornell University) · 2012
We consider infinite-horizon stationary $γ$-discounted Markov Decision Processes, for which it is known that there exists a stationary optimal policy. Using Value and Policy Iteration with some error $ε$ at each iteration, it is well-known that one can compute stationary policies that are $\frac{2γ}{(1-γ)^2}ε$-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 $\frac{2γ}{1-γ}ε$-optimal, which constitutes a significant improvement in the usual situation when $γ$ 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".