Improving Dynamic Regret in Distributed Online Mirror Descent Using Primal and Dual Information

Nima Eshraghi, Ben Liang
Proceedings of The 4th Annual Learning for Dynamics and Control Conference, PMLR 168:637-649, 2022.

Abstract

We consider the problem of distributed online optimization, with a group of learners connected via a dynamic communication graph. The goal of the learners is to track the global minimizer of a sum of time-varying loss functions in a distributed manner. We propose a novel algorithm, termed Distributed Online Mirror Descent with Multiple Averaging Decision and Gradient Consensus (DOMD-MADGC), which is based on mirror descent but incorporates multiple consensus averaging iterations over local gradients as well as local decisions. The key idea is to allow the local learners to collect a sufficient amount of global information, which enables them to more accurately approximation the time-varying global loss, so that they can closely track the dynamic global minimizer over time. We show that the dynamic regret of DOMD-MADGC is upper bounded by the path length, which is defined as the cumulative distance between successive minimizers. The resulting bound improves upon the bounds of existing distributed online algorithms and removes the explicit dependence on $T$.

Cite this Paper

BibTeX
@InProceedings{pmlr-v168-eshraghi22a, title = {Improving Dynamic Regret in Distributed Online Mirror Descent Using Primal and Dual Information}, author = {Eshraghi, Nima and Liang, Ben}, booktitle = {Proceedings of The 4th Annual Learning for Dynamics and Control Conference}, pages = {637--649}, year = {2022}, editor = {Firoozi, Roya and Mehr, Negar and Yel, Esen and Antonova, Rika and Bohg, Jeannette and Schwager, Mac and Kochenderfer, Mykel}, volume = {168}, series = {Proceedings of Machine Learning Research}, month = {23--24 Jun}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v168/eshraghi22a/eshraghi22a.pdf}, url = {https://proceedings.mlr.press/v168/eshraghi22a.html}, abstract = {We consider the problem of distributed online optimization, with a group of learners connected via a dynamic communication graph. The goal of the learners is to track the global minimizer of a sum of time-varying loss functions in a distributed manner. We propose a novel algorithm, termed Distributed Online Mirror Descent with Multiple Averaging Decision and Gradient Consensus (DOMD-MADGC), which is based on mirror descent but incorporates multiple consensus averaging iterations over local gradients as well as local decisions. The key idea is to allow the local learners to collect a sufficient amount of global information, which enables them to more accurately approximation the time-varying global loss, so that they can closely track the dynamic global minimizer over time. We show that the dynamic regret of DOMD-MADGC is upper bounded by the path length, which is defined as the cumulative distance between successive minimizers. The resulting bound improves upon the bounds of existing distributed online algorithms and removes the explicit dependence on $T$.} }
Endnote
%0 Conference Paper %T Improving Dynamic Regret in Distributed Online Mirror Descent Using Primal and Dual Information %A Nima Eshraghi %A Ben Liang %B Proceedings of The 4th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2022 %E Roya Firoozi %E Negar Mehr %E Esen Yel %E Rika Antonova %E Jeannette Bohg %E Mac Schwager %E Mykel Kochenderfer %F pmlr-v168-eshraghi22a %I PMLR %P 637--649 %U https://proceedings.mlr.press/v168/eshraghi22a.html %V 168 %X We consider the problem of distributed online optimization, with a group of learners connected via a dynamic communication graph. The goal of the learners is to track the global minimizer of a sum of time-varying loss functions in a distributed manner. We propose a novel algorithm, termed Distributed Online Mirror Descent with Multiple Averaging Decision and Gradient Consensus (DOMD-MADGC), which is based on mirror descent but incorporates multiple consensus averaging iterations over local gradients as well as local decisions. The key idea is to allow the local learners to collect a sufficient amount of global information, which enables them to more accurately approximation the time-varying global loss, so that they can closely track the dynamic global minimizer over time. We show that the dynamic regret of DOMD-MADGC is upper bounded by the path length, which is defined as the cumulative distance between successive minimizers. The resulting bound improves upon the bounds of existing distributed online algorithms and removes the explicit dependence on $T$.
APA
Eshraghi, N. & Liang, B.. (2022). Improving Dynamic Regret in Distributed Online Mirror Descent Using Primal and Dual Information. Proceedings of The 4th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 168:637-649 Available from https://proceedings.mlr.press/v168/eshraghi22a.html.

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