{"ID":2876183,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.00737","arxiv_id":"2509.00737","title":"Convergence Analysis of the PAGE Stochastic Algorithm for Weakly Convex Finite-Sum Optimization","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2509.00737","url_pdf":"https://arxiv.org/pdf/2509.00737v2","authors":"[\"Laurent Condat\",\"Peter Richtárik\"]","published":"2025-08-31T08:06:53Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.LG\"]","methods":"[]","has_code":false}