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arXiv · 2610.30143

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

Guglielmo Beretta·Tommaso Cesari·Roberto Colomboni
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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.

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Guglielmo Beretta, Tommaso Cesari, Roberto Colomboni. 2026-07-31. The Last Iterate of the Projected Stochastic Subgradient Method Pays a Logarithm, Even in Dimension One. https://arxiv.org/abs/2610.30143

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