---
title: "Last-Iterate Convergence of Stochastic Gradient Methods for Unbounded Problems"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2611.07334v1"
permalink: "https://feed.astralor.com/items/itm_3ef050dae8848e958a69409f"
published: "2026-11-05T02:17:49.000Z"
score: 55
channel: "tech"
tags: ["推理效率","RAG","Last-Iterate Convergence","Stochastic Gradient Methods","Unbounded Problems Last-iterate","Last-iterate","Under","Moreover"]
---

# Last-Iterate Convergence of Stochastic Gradient Methods for Unbounded Problems

## 速览

Last-iterate convergence guarantees for stochastic gradient methods have attracted significant attention as practical implementations typically return the last iterate instead of an average of the iterates. In this pape…

## 关键点

- Last-iterate convergence guarantees for stochastic gradient methods have attracted significant attention as practical implementations typically return the last iterate instead of an average of the iterates.
- In this paper, we study two approaches for analyzing the last-iterate convergence of proximal and projected stochastic gradient methods without bounded domain or bounded variance assumptions, where black-box variational…
- Under two related assumptions relaxing the bounded variance, we show near-optimal anytime rate $\widetilde{\mathcal{O}}(1/\sqrt{T})$ for the last iterate.

## 全文

Last-iterate convergence guarantees for stochastic gradient methods have attracted significant attention as practical implementations typically return the last iterate instead of an average of the iterates. In this paper, we study two approaches for analyzing the last-iterate convergence of proximal and projected stochastic gradient methods without bounded domain or bounded variance assumptions, where black-box variational inference serves as a running example. Under two related assumptions relaxing the bounded variance, we show near-optimal anytime rate $\widetilde{\mathcal{O}}(1/\sqrt{T})$ for the last iterate. Moreover, when the horizon $T$ is known, we remove the logarithmic factor and obtain the optimal order $\mathcal{O}(1/\sqrt{T})$, matching the order known under bounded variance or bounded domain assumptions.

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