Biased Gradient Estimate with Drastic Variance Reduction for Meta Reinforcement Learning

Despite the empirical success of meta reinforcement learning (meta-RL), there are still a number poorly-understood discrepancies between theory and practice. Critically, biased gradient estimates are almost always implemented in practice, whereas prior theory on meta-RL only establishes convergence under unbiased gradient estimates. In this work, we investigate such a discrepancy. In particular, (1) We show that unbiased gradient estimates have variance Theta(N) which linearly depends on the sample size N of the inner loop updates; (2) We propose linearized score function (LSF) gradient estimates, which have bias O(1/√N) and variance O(1/N); (3) We show that most empirical prior work in fact implements variants of the LSF gradient estimates. This implies that practical algorithms "accidentally" introduce bias to achieve better performance; (4) We establish theoretical guarantees for the LSF gradient estimates in meta-RL regarding its convergence to stationary points, showing better dependency on N than prior work when N is large.