A Variance-Reduced Cubic-Regularized Newton for Policy Optimization

• URL: http://arxiv.org/abs/2507.10120v1
• Date: Mon, 14 Jul 2025 10:04:02 GMT
• Title: A Variance-Reduced Cubic-Regularized Newton for Policy Optimization
• Authors: Cheng Sun, Zhen Zhang, Shaofu Yang,
• Abstract summary: Existing second-order methods often suffer from suboptimal sample complexity or unrealistic assumptions about importance sampling.<n>To overcome these limitations, we propose VR-CR-PN, a variance-regularized Newton-reduced estimator.<n>As an additional contribution, we introduce a novel horizon for the expected return function, allowing the algorithm to achieve a uniform sample complexity.
• Score: 6.52142708235708
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we study a second-order approach to policy optimization in reinforcement learning. Existing second-order methods often suffer from suboptimal sample complexity or rely on unrealistic assumptions about importance sampling. To overcome these limitations, we propose VR-CR-PN, a variance-reduced cubic-regularized policy Newton algorithm. To the best of our knowledge, this is the first algorithm that integrates Hessian-aided variance reduction with second-order policy optimization, effectively addressing the distribution shift problem and achieving best-known sample complexity under general nonconvex conditions but without the need for importance sampling. We theoretically establish that VR-CR-PN achieves a sample complexity of $\tilde{\mathcal{O}}(\epsilon^{-3})$ to reach an $\epsilon$-second-order stationary point, significantly improving upon the previous best result of $\tilde{\mathcal{O}}(\epsilon^{-3.5})$ under comparable assumptions. As an additional contribution, we introduce a novel Hessian estimator for the expected return function, which admits a uniform upper bound independent of the horizon length $H$, allowing the algorithm to achieve horizon-independent sample complexity.

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