On the Convergence Rate of Off-Policy Policy Optimization Methods with Density-Ratio Correction

In this paper, we study the convergence properties of off-policy policy optimization algorithms with state-action density ratio correction under function approximation setting, where the objective function is formulated as a max-max-min problem. We first clearly characterize the bias of the learning objective, and then present two strategies with finite-time convergence guarantees. In our first strategy, we propose an algorithm called P-SREDA with convergence rate O(ε^-3), whose dependency on ε is optimal. Besides, in our second strategy, we design a new off-policy actor-critic style algorithm named O-SPIM. We prove that O-SPIM converges to a stationary point with total complexity O(ε^-4), which matches the convergence rate of some recent actor-critic algorithms under on-policy setting.