Stabilizing the Q-Gradient Field for Policy Smoothness in Actor-Critic

Policies learned via continuous actor-critic methods often exhibit erratic, high-frequency oscillations, making them unsuitable for physical deployment. Current approaches attempt to enforce smoothness by directly regularizing the policy's output. We argue that this approach treats the symptom rather than the cause. In this work, we theoretically establish that policy non-smoothness is fundamentally governed by the differential geometry of the critic. By applying implicit differentiation to the actor-critic objective, we prove that the sensitivity of the optimal policy is bounded by the ratio of the Q-function's mixed-partial derivative (noise sensitivity) to its action-space curvature (signal distinctness). To empirically validate this theoretical insight, we introduce PAVE (Policy-Aware Value-field Equalization), a critic-centric regularization framework that treats the critic as a scalar field and stabilizes its induced action-gradient field. PAVE rectifies the learning signal by minimizing the Q-gradient volatility while preserving local curvature. Experimental results demonstrate that PAVE achieves smoothness and robustness comparable to policy-side smoothness regularization methods, while maintaining competitive task performance, without modifying the actor.

Enhancing Control Policy Smoothness by Aligning Actions with Predictions from Preceding States

Deep reinforcement learning has proven to be a powerful approach to solving control tasks, but its characteristic high-frequency oscillations make it difficult to apply in real-world environments. While prior methods have addressed action oscillations via architectural or loss-based methods, the latter typically depend on heuristic or synthetic definitions of state similarity to promote action consistency, which often fail to accurately reflect the underlying system dynamics. In this paper, we propose a novel loss-based method by introducing a transition-induced similar state. The transition-induced similar state is defined as the distribution of next states transitioned from the previous state. Since it utilizes only environmental feedback and actually collected data, it better captures system dynamics. Building upon this foundation, we introduce Action Smoothing by Aligning Actions with Predictions from Preceding States (ASAP), an action smoothing method that effectively mitigates action oscillations. ASAP enforces action smoothness by aligning the actions with those taken in transition-induced similar states and by penalizing second-order differences to suppress high-frequency oscillations. Experiments in Gymnasium and Isaac-Lab environments demonstrate that ASAP yields smoother control and improved policy performance over existing methods.