New Bounds for the Last Iterate of the Stochastic subGradient Method
We study the last iterate of the stochastic subgradient method for one-dimensional convex Lipschitz objectives. For a fixed horizon $n$, we consider the standard fixed stepsizes $η=Θ(1/\sqrt n)$. We prove that, for such stepsize policies, under additive i.i.d. subgradient noise with uniformly bounded variance, the last iterate features an optimization error of order $1/\sqrt n$, thereby removing the extra $(\log n)$ factor present in existing generic bounds. On the other hand, we show that without the i.i.d. assumption, the optimization error can be of order $(\log n)/\sqrt n$. Thus, under the uniformly bounded variance assumption alone, the last iterate of SsGM is suboptimal even in dime...
| Authors | Guglielmo Beretta, Tommaso Cesari, Roberto Colomboni et al. |
|---|---|
| Primary category | math.OC |
| Published | 23 June 2026 |
| Last updated at source | 23 June 2026 |
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