A Theoretical Understanding of Gradient Bias in Meta-Reinforcement Learning

Code

• github.com/Benjamin-eecs/Theoretical-GMRL
  OfficialIn paperpytorch★ 4

Abstract

Gradient-based Meta-RL (GMRL) refers to methods that maintain two-level optimisation procedures wherein the outer-loop meta-learner guides the inner-loop gradient-based reinforcement learner to achieve fast adaptations. In this paper, we develop a unified framework that describes variations of GMRL algorithms and points out that existing stochastic meta-gradient estimators adopted by GMRL are actually biased. Such meta-gradient bias comes from two sources: 1) the compositional bias incurred by the two-level problem structure, which has an upper bound of O(K^K_In||^-0.5) w.r.t. inner-loop update step K, learning rate , estimate variance ^2_In and sample size ||, and 2) the multi-step Hessian estimation bias _H due to the use of autodiff, which has a polynomial impact O((K-1)(_H)^K-1) on the meta-gradient bias. We study tabular MDPs empirically and offer quantitative evidence that testifies our theoretical findings on existing stochastic meta-gradient estimators. Furthermore, we conduct experiments on Iterated Prisoner's Dilemma and Atari games to show how other methods such as off-policy learning and low-bias estimator can help fix the gradient bias for GMRL algorithms in general.

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