Stochastic Difference-of-Convex Optimization with Momentum
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908603408973824 |
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| author | Chayti, El Mahdi Jaggi, Martin |
| author_facet | Chayti, El Mahdi Jaggi, Martin |
| contents | Stochastic difference-of-convex (DC) optimization is prevalent in numerous machine learning applications, yet its convergence properties under small batch sizes remain poorly understood. Existing methods typically require large batches or strong noise assumptions, which limit their practical use. In this work, we show that momentum enables convergence under standard smoothness and bounded variance assumptions (of the concave part) for any batch size. We prove that without momentum, convergence may fail regardless of stepsize, highlighting its necessity. Our momentum-based algorithm achieves provable convergence and demonstrates strong empirical performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17503 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic Difference-of-Convex Optimization with Momentum Chayti, El Mahdi Jaggi, Martin Machine Learning Optimization and Control Stochastic difference-of-convex (DC) optimization is prevalent in numerous machine learning applications, yet its convergence properties under small batch sizes remain poorly understood. Existing methods typically require large batches or strong noise assumptions, which limit their practical use. In this work, we show that momentum enables convergence under standard smoothness and bounded variance assumptions (of the concave part) for any batch size. We prove that without momentum, convergence may fail regardless of stepsize, highlighting its necessity. Our momentum-based algorithm achieves provable convergence and demonstrates strong empirical performance. |
| title | Stochastic Difference-of-Convex Optimization with Momentum |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2510.17503 |