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New Bounds Found for Stochastic Subgradient Method Last Iterate

By PulseAugur Editorial · [2 sources] ·

Researchers have established new theoretical bounds for the last iterate of the stochastic subgradient method (SsGM) when applied to one-dimensional convex Lipschitz objectives. The study demonstrates that with standard fixed step sizes and additive i.i.d. subgradient noise, the optimization error is of order $1/\sqrt{n}$, improving upon existing bounds by removing a logarithmic factor. However, the research also shows that without the i.i.d. assumption, the error can increase to $(\log n)/\sqrt{n}$, indicating that the last iterate of SsGM is suboptimal under certain conditions and resolving a previously open problem. AI

IMPACT Refines understanding of optimization algorithms used in machine learning, potentially improving training efficiency for certain models.

RANK_REASON The cluster contains an academic paper detailing theoretical advancements in optimization methods.

Read on arXiv cs.LG →

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New Bounds Found for Stochastic Subgradient Method Last Iterate

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COVERAGE [2]

  1. arXiv cs.LG TIER_1 English(EN) · Guglielmo Beretta, Tommaso Cesari, Roberto Colomboni, Andrea Paudice ·

    New Bounds for the Last Iterate of the Stochastic subGradient Method

    arXiv:2606.24879v1 Announce Type: cross Abstract: 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 $\eta =\Theta(1/\sqrt n)$. We prove that, for such s…

  2. arXiv cs.LG TIER_1 English(EN) · Andrea Paudice ·

    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 w…

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