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This paper addresses the overestimation bias in Q-learning when faced with large discrete action spaces, revealing that increased randomness in Q-value estimation leads to significant biases in both coupling and decoupling paradigms. The authors introduce an action intersection strategy that enables semi-decoupling, allowing two Q-functions to share trajectory data selectively, which mitigates the biases inherent in traditional methods. Experimental results demonstrate that this approach significantly outperforms state-of-the-art baselines in deep reinforcement learning settings, while also providing insights into its effectiveness through tabular experiments.
Action intersection can dynamically balance Q-value estimation biases, leading to substantial performance gains in large action spaces.
This paper considers the overestimation bias problem of Q-learning in the setting of a large action space, for the purpose of relieving the bottleneck of existing methods. We find that the large action space increases the randomness in Q-value estimation. The randomness makes two paradigms that drive the major literature on the overestimation problem have their own bottlenecks: the coupling paradigm, i.e., the optimal action and its Q-value are estimated with the same Q-function, always has a positive bias. This is because randomness leads to some actions having abnormally high estimated values than their true values, and the coupling methods prefer these actions. The decoupling paradigm, i.e., the optimal action and its Q-value are estimated with two independent Q-functions, always has a negative bias. This is because randomness increases the estimation gap between the two independent Q-tables for the same action. This paper shows that action intersection can be a simple yet powerful strategy to relieve these bottlenecks. The action intersection strategy enables semi-decoupling via two designs: (1) it allows two Q-functions to share a certain fraction of trajectory data; (2) if a data sample is shared, each Q-function is updated using the coupling paradigm; otherwise, using the decoupling paradigm. Two properties make the action intersection strategy powerful: (1) attaining a large bias range, i.e., varying the data sharing fraction, the estimation bias varies from underestimating to overestimating; (2) fine granularity: the action intersection size can be made arbitrarily finer to enable finer control. We consider two experiment settings, i.e., tabular and deep RL, deep RL experiments show that our method outperforms several SOTA baselines drastically; tabular experiments reveal why our method can achieve superior performance.
