Breaking a Logarithmic Barrier in the Stopping Time Convergence Rate of Stochastic First-order Methods
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866912485775245312 |
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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 |