Adaptive Bregman Proximal Stochastic Gradient with a Stabilized Barzilai--Borwein Step Size

• URL: http://arxiv.org/abs/2608.12009v1
• Date: Wed, 12 Aug 2026 12:46:05 GMT
• Title: Adaptive Bregman Proximal Stochastic Gradient with a Stabilized Barzilai--Borwein Step Size
• Abstract summary: Bregman finite proximal ergo gradient (BPSG) methods bring variance-reduced composite size to objectives whose geometry is poorly captured by Euclidean smoothness.<n>Their performance remains sensitive to stepwise: raw curvature estimates can fluctuate, whereas line searches add repeated searches.<n>We introduce AdaBPSG, a line-search method that combines sparse values and a non-negative matrix factorization rate.
• Score: 43.46286813814826
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Bregman proximal stochastic gradient (BPSG) methods bring variance-reduced composite optimization to objectives whose geometry is poorly captured by Euclidean smoothness. Their performance, however, remains sensitive to the step size: raw stochastic curvature estimates can fluctuate sharply, whereas line searches add repeated proximal evaluations. We introduce Ada-BPSG, a line-search-free BPSG method that couples the SAGA gradient table with a stabilized Barzilai--Borwein (BB) candidate. A mediant aggregates incremental secant information so that nearly singular local ratios receive little weight, and an explicit safeguard translates the resulting curvature estimate into the bounded step-size sequence required for convergence. This design yields a direct analytical chain from relative smoothness and component-wise variance control to convergence in finite-dimensional normed spaces. We prove an $O(n/K)$ ergodic rate for convex objectives, a restarted linear rate under relative quadratic growth, and an $O(1/K)$ bound for a Bregman proximal residual in the nonconvex setting. On logistic regression and sparse nonnegative matrix factorization, Ada-BPSG combines low objective values with substantially less sensitivity to the initial step size than standard variance-reduced baselines, while avoiding line search.

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