Multi-cut stochastic approximation methods for solving stochastic convex composite optimization

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Liang, Jiaming, Monteiro, Renato D. C., Zhang, Honghao
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866917304079482880
author Liang, Jiaming
Monteiro, Renato D. C.
Zhang, Honghao
author_facet Liang, Jiaming
Monteiro, Renato D. C.
Zhang, Honghao
contents This paper considers the stochastic convex composite optimization problem and presents multi-cut stochastic approximation (SA) methods for solving it, whose models in expectation overestimate its objective function. The multi-cut model obtained by taking the maximum of a finite number of linearizations of the stochastic objective function provides a biased estimate of the objective function, with the error being uncontrollable. Instead, our proposed SA method uses models obtained by taking the maximum of a finite number of one-cut models, i.e., suitable convex combinations of linearizations of the stochastic objective function. It is shown that the proposed methods achieve nearly optimal convergence rate and have computational performance comparable, and sometimes superior, to other SA-type methods.
format Preprint
id arxiv_https___arxiv_org_abs_2505_17463
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Multi-cut stochastic approximation methods for solving stochastic convex composite optimization
Liang, Jiaming
Monteiro, Renato D. C.
Zhang, Honghao
Optimization and Control
This paper considers the stochastic convex composite optimization problem and presents multi-cut stochastic approximation (SA) methods for solving it, whose models in expectation overestimate its objective function. The multi-cut model obtained by taking the maximum of a finite number of linearizations of the stochastic objective function provides a biased estimate of the objective function, with the error being uncontrollable. Instead, our proposed SA method uses models obtained by taking the maximum of a finite number of one-cut models, i.e., suitable convex combinations of linearizations of the stochastic objective function. It is shown that the proposed methods achieve nearly optimal convergence rate and have computational performance comparable, and sometimes superior, to other SA-type methods.
title Multi-cut stochastic approximation methods for solving stochastic convex composite optimization
topic Optimization and Control
url https://arxiv.org/abs/2505.17463