Variance-Reduced Conservative Policy Iteration

We study the sample complexity of reducing reinforcement learning to a sequence of empirical risk minimization problems over the policy space. Such reductions-based algorithms exhibit local convergence in the function space, as opposed to the parameter space for policy gradient algorithms, and thus are unaffected by the possibly non-linear or discontinuous parameterization of the policy class. We propose a variance-reduced variant of Conservative Policy Iteration that improves the sample complexity of producing a e-functional local optimum from O(epsilon(-4)) to O(epsilon(-3)). Under state-coverage and policy-completeness assumptions, the algorithm enjoys epsilon-global optimality after sampling O(epsilon(-2)) times, improving upon the previously established O(epsilon(-3)) sample requirement.