Technology Category
Search and Optimization: Sampling/Simulation-based SearchComputer Vision: Learning & Optimization for CVReasoning under Uncertainty: Stochastic Optimization
A Variance-Reduced Cubic-Regularized Newton for Policy Optimization
🤖 AI Summary
Second-order policy optimization methods in reinforcement learning suffer from suboptimal sample complexity and reliance on importance sampling, limiting their practicality and theoretical guarantees.
Method: This paper proposes VR-CR-PN—a variance-reduced cubic-regularized Newton method—introducing Hessian-driven variance reduction to second-order policy optimization for the first time. It integrates cubic regularization with a novel horizon-independent Hessian estimator, eliminating dependence on importance sampling entirely.
Results: Under non-convex policy parameterization, VR-CR-PN achieves a sample complexity of $ ilde{mathcal{O}}(varepsilon^{-3})$ to reach a first-order stationary point, improving upon the previous best-known rate of $ ilde{mathcal{O}}(varepsilon^{-3.5})$. Crucially, its Hessian estimation error admits a uniform upper bound independent of the task horizon, thereby mitigating distribution shift issues inherent in policy optimization.
Technology Category
Application Category
📝 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 $ ilde{mathcal{O}}(ε^{-3})$ to reach an $ε$-second-order stationary point, significantly improving upon the previous best result of $ ilde{mathcal{O}}(ε^{-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.
Problem
Research questions and friction points this paper is trying to address.
Improves sample complexity in second-order policy optimization
Eliminates need for unrealistic importance sampling assumptions
Addresses distribution shift in reinforcement learning algorithms
Innovation
Methods, ideas, or system contributions that make the work stand out.
Variance-reduced cubic-regularized Newton algorithm
Hessian-aided variance reduction integration
Horizon-independent Hessian estimator design
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