# Optimal Distributed Stochastic Mirror Descent for Strongly Convex Optimization

arXiv: https://arxiv.org/abs/1610.04702 · HTML: https://mlsanity.com/paper/1610.04702/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2016.

## Built on by (most cited first, 6 of 6)

- [Improving the Transient Times for Distributed Stochastic Gradient Methods](https://mlsanity.com/paper/2105.04851/) (2021)
- [On Centralized and Distributed Mirror Descent: Convergence Analysis Using Quadratic Constraints](https://mlsanity.com/paper/2105.14385/) (2021)
- [Locally Differentially Private Gradient Tracking for Distributed Online Learning over Directed Graphs](https://mlsanity.com/paper/2310.16105/) (2023)
- [No-regret learning for repeated non-cooperative games with lossy bandits](https://mlsanity.com/paper/2205.06968/) (2022)
- [Aggregation in the Mirror Space (AIMS): Fast, Accurate Distributed Machine Learning in Military Settings](https://mlsanity.com/paper/2210.16181/) (2022)
- [A New Kernel Regularity Condition for Distributed Mirror Descent: Broader Coverage and Simpler Analysis](https://mlsanity.com/paper/2603.12838/) (2026)

## Abstract (arXiv)

In this paper we consider convergence rate problems for stochastic strongly-convex optimization in the non-Euclidean sense with a constraint set over a time-varying multi-agent network. We propose two efficient non-Euclidean stochastic subgradient descent algorithms based on the Bregman divergence as distance-measuring function rather than the Euclidean distances that were employed by the standard distributed stochastic projected subgradient algorithms. For distributed optimization of nonsmooth and strongly convex functions whose only stochastic subgradients are available, the first algorithm recovers the best previous known rate of O(ln(T)/T) (where T is the total number of iterations). The second algorithm is an epoch variant of the first algorithm that attains the optimal convergence rate of O(1/T), matching that of the best previously known centralized stochastic subgradient algorithm. Finally, we report some simulation results to illustrate the proposed algorithms.