Stochastic Variance-Reduced Newton: Accelerating Finite-Sum Minimization with Large Batches

• URL: http://arxiv.org/abs/2206.02702v2
• Date: Tue, 29 Apr 2025 13:47:45 GMT
• Title: Stochastic Variance-Reduced Newton: Accelerating Finite-Sum Minimization with Large Batches
• Authors: Michał Dereziński,
• Abstract summary: We propose a finite-sum minimization algorithm that provably accelerates existing Newton methods.<n>Surprisingly, this acceleration gets more significant the larger the data size.<n>Our algorithm retains the key advantages of Newton-type methods, such as easily parallel large-batch operations and a simple unit step size.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Stochastic variance reduction has proven effective at accelerating first-order algorithms for solving convex finite-sum optimization tasks such as empirical risk minimization. Incorporating second-order information has proven helpful in further improving the performance of these first-order methods. Yet, comparatively little is known about the benefits of using variance reduction to accelerate popular stochastic second-order methods such as Subsampled Newton. To address this, we propose Stochastic Variance-Reduced Newton (SVRN), a finite-sum minimization algorithm that provably accelerates existing stochastic Newton methods from $O(\alpha\log(1/\epsilon))$ to $O\big(\frac{\log(1/\epsilon)}{\log(n)}\big)$ passes over the data, i.e., by a factor of $O(\alpha\log(n))$, where $n$ is the number of sum components and $\alpha$ is the approximation factor in the Hessian estimate. Surprisingly, this acceleration gets more significant the larger the data size $n$, which is a unique property of SVRN. Our algorithm retains the key advantages of Newton-type methods, such as easily parallelizable large-batch operations and a simple unit step size. We use SVRN to accelerate Subsampled Newton and Iterative Hessian Sketch algorithms, and show that it compares favorably to popular first-order methods with variance~reduction.

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