Convergence Analysis of the PAGE Stochastic Algorithm for Weakly Convex Finite-Sum Optimization

• URL: http://arxiv.org/abs/2509.00737v2
• Date: Sat, 20 Sep 2025 10:41:35 GMT
• Title: Convergence Analysis of the PAGE Stochastic Algorithm for Weakly Convex Finite-Sum Optimization
• Authors: Laurent Condat, Peter Richtárik,
• Abstract summary: The algorithm was designed to find stationary points of averages of work of this type.<n>It provides a continuous non-smooth case ($tautauL$) which improves between the general framework ($tautauL$) and the rate of change.
• Score: 56.57092765118707
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\tau$-weakly convex functions, which provides a continuous interpolation between the general nonconvex $L$-smooth case ($\tau = L$) and the convex case ($\tau = 0$). We establish new convergence rates for PAGE, showing that its complexity improves as $\tau$ decreases.

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