A Semismooth Newton Stochastic Proximal Point Algorithm with Variance Reduction

IF 2.6 1区 数学 Q1 MATHEMATICS, APPLIED SIAM Journal on Optimization Pub Date : 2024-03-26 DOI:10.1137/22m1488181
Andre Milzarek, Fabian Schaipp, Michael Ulbrich
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Abstract

SIAM Journal on Optimization, Volume 34, Issue 1, Page 1157-1185, March 2024.
Abstract. We develop an implementable stochastic proximal point (SPP) method for a class of weakly convex, composite optimization problems. The proposed stochastic proximal point algorithm incorporates a variance reduction mechanism and the resulting SPP updates are solved using an inexact semismooth Newton framework. We establish detailed convergence results that take the inexactness of the SPP steps into account and that are in accordance with existing convergence guarantees of (proximal) stochastic variance-reduced gradient methods. Numerical experiments show that the proposed algorithm competes favorably with other state-of-the-art methods and achieves higher robustness with respect to the step size selection.
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减少方差的半滑牛顿随机近点算法
SIAM 优化期刊》,第 34 卷第 1 期,第 1157-1185 页,2024 年 3 月。 摘要。我们针对一类弱凸复合优化问题开发了一种可实现的随机近似点(SPP)方法。所提出的随机近似点算法结合了方差缩小机制,并使用不精确的半光滑牛顿框架求解 SPP 更新。我们建立了详细的收敛结果,这些结果考虑到了 SPP 步骤的不精确性,并且与(近点)随机方差缩小梯度方法的现有收敛保证相一致。数值实验表明,所提出的算法能与其他最先进的方法相媲美,并且在步长选择方面具有更高的鲁棒性。
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来源期刊
SIAM Journal on Optimization
SIAM Journal on Optimization 数学-应用数学
CiteScore
5.30
自引率
9.70%
发文量
101
审稿时长
6-12 weeks
期刊介绍: The SIAM Journal on Optimization contains research articles on the theory and practice of optimization. The areas addressed include linear and quadratic programming, convex programming, nonlinear programming, complementarity problems, stochastic optimization, combinatorial optimization, integer programming, and convex, nonsmooth and variational analysis. Contributions may emphasize optimization theory, algorithms, software, computational practice, applications, or the links between these subjects.
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