A Theoretical Understanding of Gradient Bias in Meta-Reinforcement Learning

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 extbf{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 (KαKσ̂ In|τ|−0.5) mph{w.r.t.} inner-loop update step K, learning rate α, estimate variance σ̂ 2In and sample size |τ|, and 2) the multi-step Hessian estimation bias Δ̂ H due to the use of autodiff, which has a polynomial impact ((K−1)(Δ̂ 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.

Publication
In 2022 Conference on Neural Information Processing Systems
Jie Ren
Jie Ren
Collaborator
Luo Mai
Luo Mai
Assistant Professor

My research interests include distributed systems, machine learning, data management and quantum computing.

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