Convergence Analysis of the PAGE Stochastic Algorithm for Weakly Convex Finite-Sum Optimization
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918144706084864 |
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| author | Condat, Laurent Richtárik, Peter |
| author_facet | Condat, Laurent Richtárik, Peter |
| contents | PAGE, a stochastic algorithm introduced by Li et al. [2021], was designed to find stationary points of averages of smooth nonconvex functions. In this work, we study PAGE in the broad framework of $τ$-weakly convex functions, which provides a continuous interpolation between the general nonconvex $L$-smooth case ($τ= L$) and the convex case ($τ= 0$). We establish new convergence rates for PAGE, showing that its complexity improves as $τ$ decreases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_00737 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence Analysis of the PAGE Stochastic Algorithm for Weakly Convex Finite-Sum Optimization Condat, Laurent Richtárik, Peter Optimization and Control Machine Learning PAGE, a stochastic algorithm introduced by Li et al. [2021], was designed to find stationary points of averages of smooth nonconvex functions. In this work, we study PAGE in the broad framework of $τ$-weakly convex functions, which provides a continuous interpolation between the general nonconvex $L$-smooth case ($τ= L$) and the convex case ($τ= 0$). We establish new convergence rates for PAGE, showing that its complexity improves as $τ$ decreases. |
| title | Convergence Analysis of the PAGE Stochastic Algorithm for Weakly Convex Finite-Sum Optimization |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2509.00737 |