First-order Sobolev Reinforcement Learning
This addresses stability and efficiency issues in reinforcement learning algorithms like DDPG and SAC, though it appears incremental as it refines existing methods without altering their overall structure.
The paper tackles the problem of slow convergence and instability in temporal-difference reinforcement learning by proposing a refinement that enforces first-order Bellman consistency, training value functions to match both Bellman targets and their derivatives, which leads to faster critic convergence and more stable policy gradients.
We propose a refinement of temporal-difference learning that enforces first-order Bellman consistency: the learned value function is trained to match not only the Bellman targets in value but also their derivatives with respect to states and actions. By differentiating the Bellman backup through differentiable dynamics, we obtain analytically consistent gradient targets. Incorporating these into the critic objective using a Sobolev-type loss encourages the critic to align with both the value and local geometry of the target function. This first-order TD matching principle can be seamlessly integrated into existing algorithms, such as Q-learning or actor-critic methods (e.g., DDPG, SAC), potentially leading to faster critic convergence and more stable policy gradients without altering their overall structure.