Distributed relatively smooth optimization
File(s)
Accepted version
Author(s)
Jegnell, Sofia
Vlaski, Stefan
Type
Conference Paper
Abstract
Smoothness conditions, either on the cost itself or its gradients, are ubiquitous in the development and study of gradient-based algorithms for optimization and learning. In the context of distributed optimization and multi-agent systems, smoothness conditions and gradient bounds are additionally central to controlling the effect of local heterogeneity. We deviate from this paradigm and study distributed learning problems in relatively smooth environments, where cost functions may grow faster than a quadratic, and gradients need not be bounded. We generalize gradient noise conditions to cover this setting, and present convergence guarantees in relatively smooth and relatively convex environments. Numerical results corroborate the findings.
Date Issued
2022-12-06
Date Acceptance
2022-12-01
Citation
2022 IEEE 61st Conference on Decision and Control (CDC), 2022, pp.6511-6517
Publisher
IEEE
Start Page
6511
End Page
6517
Journal / Book Title
2022 IEEE 61st Conference on Decision and Control (CDC)
Copyright Statement
Copyright © 2023 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
http://dx.doi.org/10.1109/cdc51059.2022.9992936
Source
2022 IEEE 61st Conference on Decision and Control (CDC)
Publication Status
Published
Start Date
2022-12-06
Finish Date
2022-12-09
Coverage Spatial
Cancun, Mexico
Date Publish Online
2023-01-10