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

2026-07-11 · Source: cs.AI updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Robotics & Autonomous Systems · Depth: Expert, extended

Summary

Sanjeev Manivannan and Shuban Venkatraman introduce a novel second-order actor-critic method for discounted Markov Decision Processes (MDPs) that addresses the computational complexity and instability of traditional second-order optimization in reinforcement learning. Their approach leverages a two-timescale actor-critic framework, treating the critic as quasi-stationary during actor updates to simplify the policy Hessian decomposition. This enables the efficient use of Hessian-vector products (HVP) for curvature-aware updates. Two specific approximations, ACGN1 (Advantage-based Gauss-Newton) and ACGN2 (Intrinsic curvature), are formulated. Experiments across discrete (CartPole, LunarLander) and continuous (Reacher, Humanoid) control tasks demonstrate that ACGN2 consistently achieves faster convergence and improved sample efficiency compared to first-order (REINFORCE) and natural gradient baselines, particularly in discrete action spaces. ACGN1 also shows improvements, though with higher computational cost and sensitivity.

Key takeaway

For Machine Learning Engineers optimizing reinforcement learning agents, integrating second-order actor-critic methods, particularly ACGN2, can significantly accelerate convergence and improve sample efficiency. You should consider ACGN2 for discrete action space problems where its intrinsic curvature approximation provides stable, faster learning. For continuous or high-dimensional environments, ACGN1 or Natural Gradient Ascent might offer a more stable, albeit sometimes slower, path to higher final returns, balancing computational cost with optimization quality.

Key insights

A two-timescale actor-critic framework enables stable, efficient second-order reinforcement learning by simplifying policy Hessian estimation via quasi-stationary critic.

Principles

• Two-timescale actor-critic stabilizes second-order updates.
• Intrinsic curvature (ACGN2) offers stable, efficient updates.
• Full Hessian's interaction terms introduce high variance.

Method

The method formulates second-order actor-critic updates using Hessian-vector products (HVP) within a two-timescale framework, employing ACGN1 or ACGN2 approximations to the policy Hessian.

In practice

• ACGN2 excels in discrete control tasks like CartPole and LunarLander.
• ACGN1 and Natural Gradient offer stability in continuous, high-dimensional environments.

Topics

• Reinforcement Learning
• Actor-Critic Methods
• Second-Order Optimization
• Hessian-Vector Products
• Policy Gradient Methods
• Sample Efficiency

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.