Tight Performance Bounds for Approximate Modified Policy Iteration with Non-Stationary Policies
This work addresses a theoretical bottleneck in reinforcement learning by providing tighter performance bounds for approximate algorithms, which is incremental but impactful for high-discount scenarios.
The paper tackles the problem of improving performance guarantees in approximate dynamic programming for discounted Markov Decision Processes by considering non-stationary policies, showing that this approach can enhance bounds by a factor of O(1-γ), especially when γ is near 1, and proves the tightness of this guarantee.
We consider approximate dynamic programming for the infinite-horizon stationary $γ$-discounted optimal control problem formalized by Markov Decision Processes. While in the exact case it is known that there always exists an optimal policy that is stationary, we show that when using value function approximation, looking for a non-stationary policy may lead to a better performance guarantee. We define a non-stationary variant of MPI that unifies a broad family of approximate DP algorithms of the literature. For this algorithm we provide an error propagation analysis in the form of a performance bound of the resulting policies that can improve the usual performance bound by a factor $O(1-γ)$, which is significant when the discount factor $γ$ is close to 1. Doing so, our approach unifies recent results for Value and Policy Iteration. Furthermore, we show, by constructing a specific deterministic MDP, that our performance guarantee is tight.