Regularized diffusion adaptation via conjugate smoothing
File(s)
Accepted version
Author(s)
Vlaski, Stefan
Vandenberghe, Lieven
Sayed, Ali H
Type
Journal Article
Abstract
The purpose of this work is to develop and study a decentralized strategy for Pareto optimization of an aggregate cost consisting of regularized risks. Each risk is modeled as the expectation of some loss function with unknown probability distribution while the regularizers are assumed deterministic, but are not required to be differentiable or even continuous. The individual, regularized, cost functions are distributed across a strongly-connected network of agents and the Pareto optimal solution is sought by appealing to a multi-agent diffusion strategy. To this end, the regularizers are smoothed by means of infimal convolution and it is shown that the Pareto solution of the approximate, smooth problem can be made arbitrarily close to the solution of the original, non-smooth problem. Performance bounds are established under conditions that are weaker than assumed before in the literature, and hence applicable to a broader class of adaptation and learning problems.
Date Issued
2022-05-01
Date Acceptance
2021-05-01
Citation
IEEE Transactions on Automatic Control, 2022, 67 (5), pp.2343-2358
ISSN
0018-9286
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Start Page
2343
End Page
2358
Journal / Book Title
IEEE Transactions on Automatic Control
Volume
67
Issue
5
Copyright Statement
© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Identifier
https://ieeexplore.ieee.org/document/9435011
Subjects
math.OC
math.OC
cs.DC
cs.MA
eess.SP
stat.ML
0102 Applied Mathematics
0906 Electrical and Electronic Engineering
0913 Mechanical Engineering
Industrial Engineering & Automation
Publication Status
Published online
Date Publish Online
2021-05-18