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

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''.