Work

The Last Iterate of the Projected Stochastic Subgradient Method Pays a Logarithm, Even in Dimension One

Year: 2026

Type: preprint

Abstract: We prove that the projected stochastic subgradient method with the standard anytime stepsizes $η_t = γ/\sqrt t$ can suffer expected last-iterate optimization error of order $(\log n)/\sqrt n$ already on the real line. Combined with the classical in-expectation upper bound, this establishes the sharp worst-case order of the projected stochastic subgradient method.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.30143

Authors: Beretta, Guglielmo, Cesari, Tommaso, Colomboni, Roberto

Institutions: Aarhus University, University of Ottawa, University of Bristol

Language: English

Topic: Stochastic Gradient Optimization Techniques

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Natural Sciences and Engineering Research Council of Canada

Award: G4998900716

OpenAlex ID: W7212461765

Cites: 1

Cited by:

Related to: 10