Second-Order Actor-Critic Methods for Discounted MDPs via Policy Hessian Decomposition

2026-05-14 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Robotics & Autonomous Systems · Depth: Expert, quick

Summary

A new second-order actor-critic method has been developed for reinforcement learning (RL) in discounted reward settings. This approach addresses the limitations of first-order policy gradient methods, which often struggle with value approximation. The proposed method leverages full curvature information of the objective function by employing Hessian-vector product (HVP) computations, which are typically computationally intensive for second-order optimization in RL. Stability is achieved by treating the action-value function as locally constant with respect to policy parameters, a justification made possible within a two-timescale actor-critic framework where the critic updates faster than the actor. This framework allows the critic to be considered quasi-stationary during actor updates, leading to a computationally efficient and stable second-order update.

Key takeaway

For research scientists developing reinforcement learning algorithms, this work suggests that incorporating second-order optimization via policy Hessian decomposition can significantly improve convergence and stability. You should explore two-timescale actor-critic frameworks to justify approximations and enable efficient Hessian-vector product computations, potentially leading to more robust and faster-converging agents in discounted MDPs.

Key insights

Second-order actor-critic methods can achieve stable, efficient updates by decomposing the policy Hessian.

Principles

• Second-order methods accelerate convergence.
• Two-timescale critics stabilize actor updates.

Method

Formulate a second-order actor-critic method for discounted rewards using Hessian-vector product computations, treating the critic as quasi-stationary.

In practice

• Apply HVP for efficient curvature estimation.
• Implement two-timescale learning rates.

Topics

• Second-Order Optimization
• Actor-Critic Methods
• Policy Hessian Decomposition
• Discounted MDPs
• Hessian-Vector Product

Best for: Research Scientist, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.