[论文] A simple adaptive accelerated optimistic dual averaging method for unc...

论文概要

研究领域: ML
作者: Bowen Li, Danqing Zhou, Chuan He
发布时间: 2026-11-03
arXiv: 2611.05334

中文摘要

高效预条件在大规模一阶优化中至关重要。本文提出一种用于无约束凸优化的自适应加速乐观对偶平均（A²ODA）方法，采用基于 p-范数几何（p∈[2,∞]）的低成本预条件。该方法无需线搜索，采用基于聚合仿射下界模型的新步长选择技术。其更新结构在 p∈[2,∞] 上简单且统一，p>2 的情形不需要比欧氏情形（p=2）更精细的更新。在广义局部光滑条件下，我们导出的收敛界把常数曲率与间隙相关曲率的影响分开，后者可能带来更快衰减的项。在局部光滑的特殊情形下，该界恢复到一个近乎最优的收敛速率。

原文摘要

Efficient preconditioning plays an important role in large-scale first-order optimization. In this paper, we propose an adaptive accelerated optimistic dual averaging (\(\text{A}^2\)ODA) method for unconstrained convex optimization that adopts low-cost preconditioning based on \(p\)-norm geometry for \(p\in[2,\infty]\). The method is line-search-free and employs a new stepsize selection technique based on an aggregated affine lower model. Its update structure is simple and unified across \(p\in[2,\infty]\), with the case \(p>2\) requiring no more elaborate updates than the Euclidean case \(p=2\). Under a generalized local smoothness condition, we derive a convergence bound that separates the effects of constant and gap-dependent curvature, with the latter potentially yielding faster-decaying terms. In the special case of local smoothness, this bound recovers a nearly optimal convergence rate.

自动采集于 2026-11-05

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