Second-Order Actor-Critic Methods for Discounted MDPs via Policy Hessian Decomposition
The arXiv paper (2605.14982) explores the discounted reward framework within reinforcement learning (RL). Actor-critic techniques, which help address the difficulties of value approximation in policy gradient methods, generally utilize first-order updates and can converge to stationary points given appropriate conditions. While second-order optimization provides curvature-aware updates that can speed up convergence, its use in RL is often hindered by the complexity involved in estimating the Hessian. The authors investigate second-order approximations for the actor update that utilize comprehensive curvature data of the objective. They demonstrate that a stable approximation necessitates treating the action-value function as locally constant relative to policy parameters, a condition that is not typically valid in policy gradient methods. This approximation is better supported within a two-timescale framework.
Key facts
- Paper addresses discounted reward setting in RL
- Actor-critic methods mitigate value approximation challenges in policy gradient methods
- First-order actor-critic methods converge to stationary points under suitable assumptions
- Second-order optimization provides curvature-aware updates that accelerate convergence
- Application of second-order methods in RL is limited by computational complexity of Hessian estimation
- Authors analyze second-order approximations for the actor update using full curvature information
- Stable approximation requires treating action-value function as locally constant with respect to policy parameters
- Approximation becomes well-justified under a two-timescale framework
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