A simple adaptive accelerated optimistic dual averaging method for unconstrained convex optimization in p-norm geometry
Abstract
Efficient preconditioning plays an important role in large-scale first-order optimization. In this paper, we propose an adaptive accelerated optimistic dual averaging (A2ODA) method for unconstrained convex optimization that adopts low-cost preconditioning based on p-norm geometry for p∈[2,∞]. 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∈[2,∞], 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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BibTeX
@misc{li2026simple,
title = {{A simple adaptive accelerated optimistic dual averaging method for unconstrained convex optimization in $p$-norm geometry}},
author = {Bowen Li and Danqing Zhou and Chuan He},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05334},
eprint = {2611.05334},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05334},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A simple adaptive accelerated optimistic dual averaging method for unconstrained convex optimization in p-norm geometry
AU - Bowen Li
AU - Danqing Zhou
AU - Chuan He
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05334
UR - https://arxiv.org/abs/2611.05334
AB - Efficient preconditioning plays an important role in large-scale first-order optimization. In this paper, we propose an adaptive accelerated optimistic dual averaging (A^2ODA) method for unconstrained convex optimization that adopts low-cost preconditioning based on p-norm geometry for p∈[2,∞]. 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∈[2,∞], 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.
ER -