Cautiously Optimistic Policy Optimization and Exploration with Linear Function Approximation.

Policy optimization methods are popular reinforcement learning algorithms, because their incremental and on-policy nature makes them more stable than the value-based counterparts. However, the same properties also make them slow to converge and sample inefficient, as the on-policy requirement precludes data reuse and the incremental updates couple large iteration complexity into the sample complexity. These characteristics have been observed in experiments as well as in theory in the recent work of~\citet{agarwal2020pc}, which provides a policy optimization method PCPG that can robustly find near optimal polices for approximately linear Markov decision processes but suffers from an extremely poor sample complexity compared with value-based techniques. In this paper, we propose a new algorithm, COPOE, that overcomes the sample complexity issue of PCPG while retaining its robustness to model misspecification. Compared with PCPG, COPOE makes several important algorithmic enhancements, such as enabling data reuse, and uses more refined analysis techniques, which we expect to be more broadly applicable to designing new reinforcement learning algorithms. The result is an improvement in sample complexity from $\widetilde{O}(1/\epsilon^{11})$ for PCPG to $\widetilde{O}(1/\epsilon^3)$ for PCPG, nearly bridging the gap with value-based techniques.