Breaking a Logarithmic Barrier in the Stopping Time Convergence Rate of Stochastic First-order Methods

Fuente: arXiv
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Main Authors: Feng, Yasong, Jiang, Yifan, Wang, Tianyu, Ying, Zhiliang
Format: Preprint
Published: 2025
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author Feng, Yasong
Jiang, Yifan
Wang, Tianyu
Ying, Zhiliang
author_facet Feng, Yasong
Jiang, Yifan
Wang, Tianyu
Ying, Zhiliang
contents This work provides a novel convergence analysis for stochastic optimization in terms of stopping times, addressing the practical reality that algorithms are often terminated adaptively based on observed progress. Unlike prior approaches, our analysis: 1. Directly characterizes convergence in terms of stopping times adapted to the underlying stochastic process. 2. Breaks a logarithmic barrier in existing results. Key to our results is the development of a lemma to control the large deviation property of almost super-martingales. This lemma might be of broader interest.
format Preprint
id arxiv_https___arxiv_org_abs_2506_23335
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Breaking a Logarithmic Barrier in the Stopping Time Convergence Rate of Stochastic First-order Methods
Feng, Yasong
Jiang, Yifan
Wang, Tianyu
Ying, Zhiliang
Optimization and Control
Statistics Theory
This work provides a novel convergence analysis for stochastic optimization in terms of stopping times, addressing the practical reality that algorithms are often terminated adaptively based on observed progress. Unlike prior approaches, our analysis: 1. Directly characterizes convergence in terms of stopping times adapted to the underlying stochastic process. 2. Breaks a logarithmic barrier in existing results. Key to our results is the development of a lemma to control the large deviation property of almost super-martingales. This lemma might be of broader interest.
title Breaking a Logarithmic Barrier in the Stopping Time Convergence Rate of Stochastic First-order Methods
topic Optimization and Control
Statistics Theory
url https://arxiv.org/abs/2506.23335