A Theoretical Understanding of Gradient Bias in Meta-Reinforcement Learning

• URL: http://arxiv.org/abs/2112.15400v4
• Date: Mon, 25 Mar 2024 12:22:53 GMT
• Title: A Theoretical Understanding of Gradient Bias in Meta-Reinforcement Learning
• Authors: Xidong Feng, Bo Liu, Jie Ren, Luo Mai, Rui Zhu, Haifeng Zhang, Jun Wang, Yaodong Yang,
• Abstract summary: Gradient-based Meta-RL (GMRL) refers to methods that maintain two-level optimisation procedures. We show that existing meta-gradient estimators adopted by GMRL are actually text-bfbiased. 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.
• Score: 16.824515577815696
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 \textbf{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 $\mathcal{O}\big(K\alpha^{K}\hat{\sigma}_{\text{In}}|\tau|^{-0.5}\big)$ \emph{w.r.t.} inner-loop update step $K$, learning rate $\alpha$, estimate variance $\hat{\sigma}^{2}_{\text{In}}$ and sample size $|\tau|$, and 2) the multi-step Hessian estimation bias $\hat{\Delta}_{H}$ due to the use of autodiff, which has a polynomial impact $\mathcal{O}\big((K-1)(\hat{\Delta}_{H})^{K-1}\big)$ 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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