Improved Rates for Stochastic Variance-Reduced Difference-of-Convex Algorithms
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909788330262528 |
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| author | Nguyen, Anh Duc Yurtsever, Alp Sra, Suvrit Toh, Kim-Chuan |
| author_facet | Nguyen, Anh Duc Yurtsever, Alp Sra, Suvrit Toh, Kim-Chuan |
| contents | In this work, we propose and analyze DCA-PAGE, a novel algorithm that integrates the difference-of-convex algorithm (DCA) with the ProbAbilistic Gradient Estimator (PAGE) to solve structured nonsmooth difference-of-convex programs. In the finite-sum setting, our method achieves a gradient computation complexity of $O(N + N^{1/2}\varepsilon^{-2})$ with sample size $N$, surpassing the previous best-known complexity of $O(N + N^{2/3}\varepsilon^{-2})$ for stochastic variance-reduced (SVR) DCA methods. Furthermore, DCA-PAGE readily extends to online settings with a similar optimal gradient computation complexity $O(b + b^{1/2}\varepsilon^{-2})$ with batch size $b$, a significant advantage over existing SVR DCA approaches that only work for the finite-sum setting. We further refine our analysis with a gap function, which enables us to obtain comparable convergence guarantees under milder assumptions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_11657 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Improved Rates for Stochastic Variance-Reduced Difference-of-Convex Algorithms Nguyen, Anh Duc Yurtsever, Alp Sra, Suvrit Toh, Kim-Chuan Optimization and Control In this work, we propose and analyze DCA-PAGE, a novel algorithm that integrates the difference-of-convex algorithm (DCA) with the ProbAbilistic Gradient Estimator (PAGE) to solve structured nonsmooth difference-of-convex programs. In the finite-sum setting, our method achieves a gradient computation complexity of $O(N + N^{1/2}\varepsilon^{-2})$ with sample size $N$, surpassing the previous best-known complexity of $O(N + N^{2/3}\varepsilon^{-2})$ for stochastic variance-reduced (SVR) DCA methods. Furthermore, DCA-PAGE readily extends to online settings with a similar optimal gradient computation complexity $O(b + b^{1/2}\varepsilon^{-2})$ with batch size $b$, a significant advantage over existing SVR DCA approaches that only work for the finite-sum setting. We further refine our analysis with a gap function, which enables us to obtain comparable convergence guarantees under milder assumptions. |
| title | Improved Rates for Stochastic Variance-Reduced Difference-of-Convex Algorithms |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2509.11657 |