Composite and Stochastic Smoothed Decentralized Bregman Proximal-Gradient Methods
Abstract
Smoothed decentralized Bregman proximal-gradient (SDBPG) methods combine relative-smoothness geometry with edge-dual consensus. We extend SDBPG to node-specific convex nonsmooth regularizers and unbiased stochastic local gradients while retaining its Bregman primal-dual smoothing mechanism. The analysis isolates temporal subgradient motion and aggregation mismatch as two defect sequences. For trajectories in a forward-invariant compact subset of the kernel domain and admissible parameters, finite accumulated defects yield an O(T−1) bound on the squared best-iterate proximal residual over T iterations. The stochastic bound separates accumulated oracle variance from expected defects and attains the same order when the variance bounds and expected defects are summable. Common active-structure identification, together with local subgradient conditions, gives sufficient finite-defect conditions for ℓ1 and group ℓ2,1 regularization. Experiments with common regularizers and heterogeneous sensing operators relate defect decay to observed support stabilization and compare reconstruction and communication with decentralized proximal and gradient-tracking methods. A separate phase-retrieval study evaluates the effect of a quartic Bregman kernel. Code and experiment scripts are available at https://github.com/shengze-xu/composite-stochastic-sdbpg .
Related
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BibTeX
@misc{xu2026composite,
title = {{Composite and Stochastic Smoothed Decentralized Bregman Proximal-Gradient Methods}},
author = {Shengze Xu and Chenhan Jin and Qingsong Wang and Tieyong Zeng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18231},
eprint = {2610.18231},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18231},
}
RIS
TY - UNPB
TI - Composite and Stochastic Smoothed Decentralized Bregman Proximal-Gradient Methods
AU - Shengze Xu
AU - Chenhan Jin
AU - Qingsong Wang
AU - Tieyong Zeng
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18231
UR - https://arxiv.org/abs/2610.18231
AB - Smoothed decentralized Bregman proximal-gradient (SDBPG) methods combine relative-smoothness geometry with edge-dual consensus. We extend SDBPG to node-specific convex nonsmooth regularizers and unbiased stochastic local gradients while retaining its Bregman primal-dual smoothing mechanism. The analysis isolates temporal subgradient motion and aggregation mismatch as two defect sequences. For trajectories in a forward-invariant compact subset of the kernel domain and admissible parameters, finite accumulated defects yield an O(T^−1) bound on the squared best-iterate proximal residual over T iterations. The stochastic bound separates accumulated oracle variance from expected defects and attains the same order when the variance bounds and expected defects are summable. Common active-structure identification, together with local subgradient conditions, gives sufficient finite-defect conditions for ℓ_1 and group ℓ_2,1 regularization. Experiments with common regularizers and heterogeneous sensing operators relate defect decay to observed support stabilization and compare reconstruction and communication with decentralized proximal and gradient-tracking methods. A separate phase-retrieval study evaluates the effect of a quartic Bregman kernel. Code and experiment scripts are available at https://github.com/shengze-xu/composite-stochastic-sdbpg .
ER -