Variance Reduction and Low Sample Complexity in Stochastic Optimization via Proximal Point Method
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914213175230464 |
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| author | Liang, Jiaming |
| author_facet | Liang, Jiaming |
| contents | High-probability guarantees in stochastic optimization are often obtained only under strong noise assumptions such as sub-Gaussian tails. We show that such guarantees can also be achieved under the weaker assumption of bounded variance by developing a stochastic proximal point method. This method combines a proximal subproblem solver, which inherently reduces variance, with a probability booster that amplifies per-iteration reliability into high-confidence results. The analysis demonstrates convergence with low sample complexity, without restrictive noise assumptions or reliance on mini-batching. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_08992 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variance Reduction and Low Sample Complexity in Stochastic Optimization via Proximal Point Method Liang, Jiaming Optimization and Control Machine Learning High-probability guarantees in stochastic optimization are often obtained only under strong noise assumptions such as sub-Gaussian tails. We show that such guarantees can also be achieved under the weaker assumption of bounded variance by developing a stochastic proximal point method. This method combines a proximal subproblem solver, which inherently reduces variance, with a probability booster that amplifies per-iteration reliability into high-confidence results. The analysis demonstrates convergence with low sample complexity, without restrictive noise assumptions or reliance on mini-batching. |
| title | Variance Reduction and Low Sample Complexity in Stochastic Optimization via Proximal Point Method |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2402.08992 |