# MUSIC: Accelerated Convergence for Distributed Optimization With Inexact and Exact Methods

arXiv: https://arxiv.org/abs/2403.02589 · HTML: https://mlsanity.com/paper/2403.02589/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 57 references that are in the map.
- First posted on arXiv 5 Mar 2024.

## Builds on (most cited first, 29 of 29)

- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [Tighter Theory for Local SGD on Identical and Heterogeneous Data](https://mlsanity.com/paper/1909.04746/) (2019)
- [EXTRA: An Exact First-Order Algorithm for Decentralized Consensus Optimization](https://mlsanity.com/paper/1404.6264/) (2014)
- [On the Convergence of Decentralized Gradient Descent](https://mlsanity.com/paper/1310.7063/) (2013)
- [Achieving Geometric Convergence for Distributed Optimization over Time-Varying Graphs](https://mlsanity.com/paper/1607.03218/) (2016)
- [Distributed Stochastic Gradient Tracking Methods](https://mlsanity.com/paper/1805.11454/) (2018)
- [Distributed optimization over time-varying directed graphs](https://mlsanity.com/paper/1303.2289/) (2013)
- [An Improved Analysis of Gradient Tracking for Decentralized Machine Learning](https://mlsanity.com/paper/2202.03836/) (2022)
- [A decentralized proximal-gradient method with network independent step-sizes and separated convergence rates](https://mlsanity.com/paper/1704.07807/) (2017)
- [Exact Diffusion for Distributed Optimization and Learning --- Part I: Algorithm Development](https://mlsanity.com/paper/1702.05122/) (2017)
- [Optimal and Practical Algorithms for Smooth and Strongly Convex Decentralized Optimization](https://mlsanity.com/paper/2006.11773/) (2020)
- [On the Influence of Bias-Correction on Distributed Stochastic Optimization](https://mlsanity.com/paper/1903.10956/) (2019)
- [Stochastic Gradient-Push for Strongly Convex Functions on Time-Varying Directed Graphs](https://mlsanity.com/paper/1406.2075/) (2014)
- [Decentralized Gradient Tracking with Local Steps](https://mlsanity.com/paper/2301.01313/) (2023)
- [Accelerated Distributed Nesterov Gradient Descent](https://mlsanity.com/paper/1705.07176/) (2017)
- [Balancing Communication and Computation in Distributed Optimization](https://mlsanity.com/paper/1709.02999/) (2017)
- [Decentralized Proximal Gradient Algorithms with Linear Convergence Rates](https://mlsanity.com/paper/1909.06479/) (2019)
- [A Class of Prediction-Correction Methods for Time-Varying Convex Optimization](https://mlsanity.com/paper/1509.05196/) (2015)
- [Exact Diffusion for Distributed Optimization and Learning --- Part II: Convergence Analysis](https://mlsanity.com/paper/1702.05142/) (2017)
- [Revisiting EXTRA for Smooth Distributed Optimization](https://mlsanity.com/paper/2002.10110/) (2020)
- [Accelerated Gradient Tracking over Time-varying Graphs for Decentralized Optimization](https://mlsanity.com/paper/2104.02596/) (2021)
- [Geometrically Convergent Distributed Optimization with Uncoordinated Step-Sizes](https://mlsanity.com/paper/1609.05877/) (2016)
- [Distributed stochastic gradient tracking algorithm with variance reduction for non-convex optimization](https://mlsanity.com/paper/2106.14479/) (2021)
- [Decentralized Prediction-Correction Methods for Networked Time-Varying Convex Optimization](https://mlsanity.com/paper/1602.01716/) (2016)
- [Distributed Subgradient Projection Algorithm over Directed Graphs: Alternate Proof](https://mlsanity.com/paper/1706.07707/) (2017)
- [Distributed Constrained Optimization with Delayed Subgradient Information over Time-Varying Network under Adaptive Quantization](https://mlsanity.com/paper/2106.08271/) (2021)

## Abstract (arXiv)

Gradient-type distributed optimization methods have blossomed into one of the most important tools for solving a minimization learning task over a networked agent system. However, only one gradient update per iteration is difficult to achieve a substantive acceleration of convergence. In this paper, we propose an accelerated framework named as MUSIC allowing each agent to perform multiple local updates and a single combination in each iteration. More importantly, we equip inexact and exact distributed optimization methods into this framework, thereby developing two new algorithms that exhibit accelerated linear convergence and high communication efficiency. Our rigorous convergence analysis reveals the sources of steady-state errors arising from inexact policies and offers effective solutions. Numerical results based on synthetic and real datasets demonstrate both our theoretical motivations and analysis, as well as performance advantages.