  We revisit the stochastic variance-reduced policy gradient (SVRPG) method
proposed by Papini et al. (2018) for reinforcement learning. We provide an
improved convergence analysis of SVRPG and show that it can find an
$\epsilon$-approximate stationary point of the performance function within
$O(1/\epsilon^{5/3})$ trajectories. This sample complexity improves upon the
best known result $O(1/\epsilon^2)$ by a factor of $O(1/\epsilon^{1/3})$. At
the core of our analysis is (i) a tighter upper bound for the variance of
importance sampling weights, where we prove that the variance can be controlled
by the parameter distance between different policies; and (ii) a fine-grained
analysis of the epoch length and batch size parameters such that we can
significantly reduce the number of trajectories required in each iteration of
SVRPG. We also empirically demonstrate the effectiveness of our theoretical
claims of batch sizes on reinforcement learning benchmark tasks.
