---
title: "A simple adaptive accelerated optimistic dual averaging method for unconstrained convex optimization in $p$-norm geometry"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2611.05334v1"
permalink: "https://feed.astralor.com/items/itm_c9c21ca54e07fe7257c88bb2"
published: "2026-11-03T18:35:20.000Z"
score: 56
channel: "tech"
tags: ["RAG","Efficient","ODA","Its","Euclidean","Under"]
---

# A simple adaptive accelerated optimistic dual averaging method for unconstrained convex optimization in $p$-norm geometry

## At a glance

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 op…

## Key points

- 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,\inf…
- The method is line-search-free and employs a new stepsize selection technique based on an aggregated affine lower model.

## Full text

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.

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