Work

Convergence Analysis of the ProbAbilistic Gradient Estimator Algorithm for Weakly Convex Finite-Sum Optimization

Year: 2026

Type: article

Abstract: The ProbAbilistic Gradient Estimator algorithm (PAGE), a stochastic algorithm introduced by Li et al. in 2021, was designed to find stationary points for the average of smooth nonconvex functions. In this work, we study PAGE within the broad framework of $$\tau $$ -weakly convex functions, providing a continuous interpolation between the general nonconvex L-smooth regime ( $$\tau =L$$ ) and the convex regime ( $$\tau =0$$ ). We establish new convergence rates for PAGE, showing that its complexity improves as $$\tau $$ decreases.

Source: Journal of Optimization Theory and Applications

DOI: 10.1007/s10957-026-03065-4

Authors: Laurent Condat, Peter Richtárik

Institution: King Abdullah University of Science and Technology

Language: English

Topic: Stochastic Gradient Optimization Techniques

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: King Abdullah University of Science and Technology