# Distributed Optimization over Time-varying Graphs with Imperfect Sharing of Information

arXiv: https://arxiv.org/abs/2106.08469 · HTML: https://mlsanity.com/paper/2106.08469/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2021.

## Built on by (most cited first, 5 of 5)

- [On the Convergence of Decentralized Federated Learning Under Imperfect Information Sharing](https://mlsanity.com/paper/2303.10695/) (2023)
- [FedNMUT -- Federated Noisy Model Update Tracking Convergence Analysis](https://mlsanity.com/paper/2403.13247/) (2024)
- [Logarithmically Quantized Distributed Optimization over Dynamic Multi-Agent Networks](https://mlsanity.com/paper/2410.20345/) (2024)
- [Distributed Unconstrained Optimization with Time-varying Cost Functions](https://mlsanity.com/paper/2212.09472/) (2022)
- [Convex and Non-convex Federated Learning with Stale Stochastic Gradients: Diminishing Step Size is All You Need](https://mlsanity.com/paper/2603.02639/) (2026)

## Abstract (arXiv)

We study strongly convex distributed optimization problems where a set of agents are interested in solving a separable optimization problem collaboratively. In this paper, we propose and study a two time-scale decentralized gradient descent algorithm for a broad class of lossy sharing of information over time-varying graphs. One time-scale fades out the (lossy) incoming information from neighboring agents, and one time-scale regulates the local loss functions' gradients. For strongly convex loss functions, with a proper choice of step-sizes, we show that the agents' estimates converge to the global optimal state at a rate of O(T-1/2). Another important contribution of this work is to provide novel tools to deal with diminishing average weights over time-varying graphs.