Biased Gradient Estimate with Drastic Variance Reduction for Meta Reinforcement Learning
This addresses a foundational issue in meta-RL by explaining why biased methods work better in practice, potentially improving algorithm design and theoretical understanding for researchers.
The paper tackled the discrepancy between theory and practice in meta-RL by showing that unbiased gradient estimates have high variance scaling linearly with sample size, and proposed a biased gradient estimate with reduced variance and bias, establishing better convergence guarantees for large sample sizes.
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 $Θ(N)$ 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 $\mathcal{O}(1/\sqrt{N})$ and variance $\mathcal{O}(1/N)$; (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.