A Meta-Learning Approach to Mitigating the Estimation Bias of Q-Learning

Abstract

It is a longstanding problem that Q-learning suffers from the overestimation bias. This issue originates from the fact that Q-learning uses the expectation of maximum Q-value to approximate the maximum expected Q-value. A number of algorithms, such as Double Q-learning, were proposed to address this problem by reducing the estimation of maximum Q-value, but this may lead to an underestimation bias. Note that this underestimation bias may have a larger performance penalty than the overestimation bias. Different from previous algorithms, this article studies this issue from a fresh perspective, i.e., meta-learning view, which leads to our Meta-Debias Q-learning. The main idea is to extract the maximum expected Q-value with meta-learning over multiple tasks to remove the estimation bias of maximum Q-value and help the agent choose the optimal action more accurately. However, there are two challenges: (1) How to automatically select suitable training tasks? (2) How to positively transfer the meta-knowledge from selected tasks to remove the estimation bias of maximum Q-value? To address the two challenges mentioned above, we quantify the similarity between the training tasks and the test task. This similarity enables us to select appropriate “partial” training tasks and helps the agent extract the maximum expected Q-value to remove the estimation bias. Extensive experiment results show that our Meta-Debias Q-learning outperforms SOTA baselines drastically in three evaluation indicators, i.e., maximum Q-value, policy, and reward. More specifically, our Meta-Debias Q-learning only underestimates \(1.2*10^{-3}\) than the maximum expected Q-value in the multi-armed bandit environment and only differs \(5.04\%-5\%=0.04\%\) than the optimal policy in the two states MDP environment. In addition, we compare the uniform weight and our similarity weight. Experiment results reveal fundamental insights into why our proposed algorithm outperforms in the maximum Q-value, policy, and reward.