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

Researchers present PAVE, a theoretical and practical framework addressing policy instability in actor-critic reinforcement learning by stabilizing the critic's Q-function gradient field rather than directly regularizing policy outputs. The work demonstrates that policy smoothness is fundamentally determined by the critic's differential geometry, offering a more principled approach to deploying learned policies in physical systems.

This research tackles a fundamental challenge in continuous control reinforcement learning: policies trained via actor-critic methods often exhibit erratic oscillations incompatible with real-world robotic or mechanical systems. Traditional solutions attempt to smooth policies directly through output regularization, addressing symptoms rather than root causes. The authors establish through theoretical analysis that policy non-smoothness stems from the critic's mathematical structure, specifically the relationship between its mixed-partial derivatives and action-space curvature.

The contribution lies in formalizing this relationship via implicit differentiation applied to the actor-critic objective. By bounding optimal policy sensitivity to these geometric properties, the researchers reframe the problem from policy-centric to value-centric optimization. This theoretical insight motivates PAVE, which treats the Q-function as a scalar field and minimizes gradient volatility while preserving curvature information—essentially conditioning the learning signal before it reaches the actor.

For the reinforcement learning and robotics communities, this represents a meaningful methodological shift. Rather than constrain the actor network's outputs or apply post-hoc smoothing, PAVE operates upstream in the value learning process. This enables deployment of smoother policies without architectural modifications or performance sacrifices. The approach appeals to practitioners developing autonomous systems where erratic control signals can cause mechanical wear, energy inefficiency, or safety issues.

The research opens avenues for deeper investigation into value function geometry's role in learning quality. Future work might explore how these principles extend to discrete action spaces, hierarchical control architectures, or multi-agent settings where coordinated smooth behavior becomes critical.

• →Policy smoothness in actor-critic methods is fundamentally governed by the critic's differential geometry, not the policy architecture itself.
• →PAVE regularizes the critic's Q-gradient field to reduce volatility while preserving action-space curvature, achieving smoothness without modifying the actor.
• →Theoretical analysis bounds policy sensitivity to the ratio of the Q-function's noise sensitivity and signal distinctness.
• →The approach maintains competitive task performance while producing smoother control signals suitable for physical deployment.
• →This research shifts emphasis from policy-side regularization to critic-centric optimization in continuous control learning.