Revisiting Temporal Regularization for Smooth Control in Deep Reinforcement Learning

This paper proposes a novel regularization design to effectively smooth policy functions in reinforcement learning. While regularization that enhances global'' Lipschitz continuity was initially considered, it has been limited to local'' Lipschitz continuity due to a tradeoff between smoothness and expressiveness. However, it has become apparent that the original implementation is cumbersome and does not provide sufficient smoothing, leading to a preference for simpler implementations. This stems from a discrepancy between theory and implementation, and a more appropriate implementation can expect to facilitate smoothing. Therefore, this paper identifies three reasons why the original implementation does not function adequately and provide remedies for them. This modified regularization performs well across multiple tasks and algorithms, successfully achieving smooth motion while improving control performance. Furthermore, by applying it to sim-to-real reinforcement learning for a quadruped robot, it is demonstrated that smooth motion provides robustness against sudden changes in target velocity commands.

Reinforcement learning often produces high-frequency oscillatory control signals that undermine the safety and stability required for physical deployment. Explicit action chunking addresses this by predicting fixed-horizon trajectories but scales the policy output dimension proportionally with the horizon length, leading to optimization difficulties and incompatibility with standard step-wise interaction. To overcome these challenges, this paper proposes Dual-Window Smoothing (DWS), an implicit action chunking framework for smooth continuous control. Unlike explicit methods, DWS enforces temporal coherence without expanding the action space. It uses a dual-window design: an execution window that ensures physical smoothness through deterministic modulation, and a value window that aligns temporal-difference targets over the horizon to correct critic bias caused by open-loop execution. DWS also includes a lightweight actor-side temporal regularizer based on first-order action differences to promote global continuity. This design effectively bridges the gap between temporal abstraction and reactive step-wise control. Experiments on benchmarks including the DeepMind Control Suite and industrial energy management tasks show that DWS outperforms state-of-the-art (SOTA) baselines. In complex vision-based autonomous driving tasks, DWS achieves smoother control, safer behavior with reduced jitter, and attains a 100% success rate.

Actor-critic methods achieve strong performance in continuous control, but their policies can produce highly oscillatory actions. A common remedy is to add auxiliary smoothness losses. However, their contribution can be negligible when their gradients are small relative to the native actor gradient. Moreover, existing methods often combine multiple auxiliary losses, complicating loss balancing without necessarily improving the return-smoothness trade-off. We introduce DAMPER (Direction-Aware Magnitude-Controlled Projection with Explicit Return Priority), which combines the native actor gradient with a temporal-consistency gradient through conflict-conditioned projection and adaptive magnitude control. It removes the auxiliary component opposing the actor gradient and scales the retained temporal direction relative to the actor gradient norm, preserving positive alignment with the native actor gradient. Experiments with TD3 and SAC on six continuous-control tasks show reduced action oscillation relative to the native agents in all 12 task-backbone pairs and the best oscillation score among the compared methods in eight, with task-dependent return trade-offs.