# Optimal Distributed Optimization on Slowly Time-Varying Graphs

arXiv: https://arxiv.org/abs/1805.06045 · HTML: https://mlsanity.com/paper/1805.06045/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2018.

## Built on by (most cited first, 3 of 3)

- [ADOM: Accelerated Decentralized Optimization Method for Time-Varying Networks](https://mlsanity.com/paper/2102.09234/) (2021)
- [Accelerated Gradient Tracking over Time-varying Graphs for Decentralized Optimization](https://mlsanity.com/paper/2104.02596/) (2021)
- [Near-Optimal Decentralized Stochastic Convex Optimization over Networks](https://mlsanity.com/paper/2606.04757/) (2026)

## Abstract (arXiv)

We study optimal distributed first-order optimization algorithms when the network (i.e., communication constraints between the agents) changes with time. This problem is motivated by scenarios where agents experience network malfunctions. We provide a sufficient condition that guarantees a convergence rate with optimal (up lo logarithmic terms) dependencies on the network and function parameters if the network changes are constrained to a small percentage α of the total number of iterations. We call such networks slowly time-varying networks. Moreover, we show that Nesterov's method has an iteration complexity of Omega big( big(√kappa_Phi · barchi + α log(kappa_Phi · barchi)big) log(1 / varepsilon)big) for decentralized algorithms, where kappa_Phi is condition number of the objective function, and barchi is a worst case bound on the condition number of the sequence of communication graphs. Additionally, we provide an explicit upper bound on α in terms of the condition number of the objective function and network topologies.