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

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 e at each iteration, it is well-known that one can compute stationary policies that are 2γ/(1 - γ)2 e-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 2γ/1-γ e-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".