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

arXiv: https://arxiv.org/abs/2112.03504 · HTML: https://mlsanity.com/paper/2112.03504/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2021.

## Built on by (most cited first, 7 of 7)

- [Online Federated Learning via Non-Stationary Detection and Adaptation amidst Concept Drift](https://mlsanity.com/paper/2211.12578/) (2022)
- [Locally Differentially Private Online Federated Learning With Correlated Noise](https://mlsanity.com/paper/2411.18752/) (2024)
- [Dynamic Regret Analysis of Safe Distributed Online Optimization for Convex and Non-convex Problems](https://mlsanity.com/paper/2302.12320/) (2023)
- [A Survey on Distributed Online Optimization and Game](https://mlsanity.com/paper/2205.00473/) (2022)
- [Optimized Gradient Tracking for Decentralized Online Learning](https://mlsanity.com/paper/2306.06375/) (2023)
- [Differentially Private Online Federated Learning with Correlated Noise](https://mlsanity.com/paper/2403.16542/) (2024)
- [A Hybrid Stochastic Gradient Tracking Method for Distributed Online Optimization Over Time-Varying Directed Networks](https://mlsanity.com/paper/2508.20645/) (2025)

## Abstract (arXiv)

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.