A²ODA method achieves accelerated convergence in p-norm geometry
Original title: A simple adaptive accelerated optimistic dual averaging method for unconstrained convex optimization in $p$-norm geometry
Adaptive accelerated optimistic dual averaging provides line-search-free preconditioning for convex optimization.
The paper introduces A²ODA, an adaptive accelerated optimistic dual averaging method for unconstrained convex optimization. It uses p-norm geometry preconditioning for p between 2 and infinity. The method features a new stepsize selection and unified updates. Under generalized local smoothness, it derives a convergence bound separating constant and gap-dependent curvature terms.
- Proposed for p in [2, ∞]
- Line-search-free with aggregated affine lower model
- Convergence bound separates constant and gap-dependent curvature
- Recovers nearly optimal rate in local smoothness case
From the original article
1 min read at arxiv.orgEfficient 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 $p\in[2,\infty]$.
By Bowen Li · arxiv.org
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