Last-Iterate Convergence of Clipped SGD with Linear Decay
In this paper, we study the last-iterate convergence of clipped stochastic gradient descent under heavy-tailed noise. We assume that the stochastic gradients are unbiased and that the noise has a bounded central $p$-th moment, where $1<p\le2$. For smooth convex objectives, a linearly decreasing learning rate gives a high-probability error bound of order $O(LR^2\log(1/δ)/T+σR(\log(1/δ)/T)^{(p-1)/p})$. We further establish last-iterate guarantees for nonsmooth composite objectives and smooth composite objectives with proximal updates. In addition, when a causal adversary replaces at most $q$ gradients, the same clipped update achieves a bound with $\log(1/δ)$ replaced by $\log(1/δ)+q$. The ...
| Authors | Wei Jiang, Haomin Bai, Zechao Li |
|---|---|
| Primary category | cs.LG |
| Published | 13 October 2026 |
| Last updated at source | 13 October 2026 |
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