Finite Sample Analysis of Two-Time-Scale Natural Actor-Critic Algorithm
This provides theoretical guarantees for a popular reinforcement learning method, addressing a gap in understanding for researchers and practitioners, though it is incremental as it builds on existing algorithms.
The paper tackles the theoretical understanding of two-time-scale natural actor-critic algorithms in reinforcement learning by analyzing their global convergence in the tabular setting using a single trajectory, achieving a sample complexity of $ ilde{\mathcal{O}}(1/\delta^{8})$ with fixed exploration and improving to $ ilde{\mathcal{O}}(1/\delta^{6})$ with decreasing exploration.
Actor-critic style two-time-scale algorithms are one of the most popular methods in reinforcement learning, and have seen great empirical success. However, their performance is not completely understood theoretically. In this paper, we characterize the \emph{global} convergence of an online natural actor-critic algorithm in the tabular setting using a single trajectory of samples. Our analysis applies to very general settings, as we only assume ergodicity of the underlying Markov decision process. In order to ensure enough exploration, we employ an $ε$-greedy sampling of the trajectory. For a fixed and small enough exploration parameter $ε$, we show that the two-time-scale natural actor-critic algorithm has a rate of convergence of $\tilde{\mathcal{O}}(1/T^{1/4})$, where $T$ is the number of samples, and this leads to a sample complexity of $\Tilde{\mathcal{O}}(1/δ^{8})$ samples to find a policy that is within an error of $δ$ from the \emph{global optimum}. Moreover, by carefully decreasing the exploration parameter $ε$ as the iterations proceed, we present an improved sample complexity of $\Tilde{\mathcal{O}}(1/δ^{6})$ for convergence to the global optimum.