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Advantage learning (AL) aims to improve the robustness of value-based reinforcement learning against estimation errors with action-gap-based regularization. Unfortunately, the method tends to be unstable in the case of function approximation. In this paper, we propose a simple variant of AL, named smoothing advantage learning (SAL), to alleviate this problem. The key to our method is to replace the original Bellman Optimal operator in AL with a smooth one so as to obtain more reliable estimation of the temporal difference target. We give a detailed account of the resulting action gap and the performance bound for approximate SAL. Further theoretical analysis reveals that the proposed value smoothing technique not only helps to stabilize the training procedure of AL by controlling the trade-off between convergence rate and the upper bound of the approximation errors, but is beneficial to increase the action gap between the optimal and sub-optimal action value as well.

Advantage Learning (AL) seeks to increase the action gap between the optimal action and its competitors, so as to improve the robustness to estimation errors. However, the method becomes problematic when the optimal action induced by the approximated value function does not agree with the true optimal action. In this paper, we present a novel method, named clipped Advantage Learning (clipped AL), to address this issue. The method is inspired by our observation that increasing the action gap blindly for all given samples while not taking their necessities into account could accumulate more errors in the performance loss bound, leading to a slow value convergence, and to avoid that, we should adjust the advantage value adaptively. We show that our simple clipped AL operator not only enjoys fast convergence guarantee but also retains proper action gaps, hence achieving a good balance between the large action gap and the fast convergence. The feasibility and effectiveness of the proposed method are verified empirically on several RL benchmarks with promising performance.

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