PLADOS: A Parameter-free Landing Algorithm for Decentralized Optimization on the Stiefel Manifold
Abstract
Decentralized optimization on the Stiefel manifold has broad applications in machine learning and signal processing. We propose PLADOS, a parameter-free landing algorithm for decentralized optimization on the Stiefel manifold. Each iteration combines local stochastic gradient updates with a single retraction-free communication step over the communication graph. A key convex-like property of the intersection of the nonconvex Stiefel manifold and consensus constraints is characterized through a restricted secant inequality for the penalty-only scheme, ensuring local contraction of the manifold consensus error without introducing additional parameters that require tuning. For n nodes using independent local batches of size b, we prove that PLADOS achieves linear speedup with respect to the number of nodes with an asymptotic convergence rate of O(σ/√(nbK)+(nξ2)1/3/K2/3) after K iterations, where σ2>0 is the sampling variance and ξ2 quantifies gradient heterogeneity. Experiments demonstrate stability across tested stepsizes and networks, time efficiency, and linear speedup with respect to the number of nodes.
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BibTeX
@misc{li2026plados,
title = {{PLADOS: A Parameter-free Landing Algorithm for Decentralized Optimization on the Stiefel Manifold}},
author = {Shu Li and Jiang Hu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07750},
eprint = {2610.07750},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07750},
}
RIS
TY - UNPB
TI - PLADOS: A Parameter-free Landing Algorithm for Decentralized Optimization on the Stiefel Manifold
AU - Shu Li
AU - Jiang Hu
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.07750
UR - https://arxiv.org/abs/2610.07750
AB - Decentralized optimization on the Stiefel manifold has broad applications in machine learning and signal processing. We propose PLADOS, a parameter-free landing algorithm for decentralized optimization on the Stiefel manifold. Each iteration combines local stochastic gradient updates with a single retraction-free communication step over the communication graph. A key convex-like property of the intersection of the nonconvex Stiefel manifold and consensus constraints is characterized through a restricted secant inequality for the penalty-only scheme, ensuring local contraction of the manifold consensus error without introducing additional parameters that require tuning. For n nodes using independent local batches of size b, we prove that PLADOS achieves linear speedup with respect to the number of nodes with an asymptotic convergence rate of O(σ/√(nbK)+(nξ^2)^1/3/K^2/3) after K iterations, where σ^2>0 is the sampling variance and ξ^2 quantifies gradient heterogeneity. Experiments demonstrate stability across tested stepsizes and networks, time efficiency, and linear speedup with respect to the number of nodes.
ER -