# Decentralized optimization with non-identical sampling in presence of stragglers

arXiv: https://arxiv.org/abs/2108.11071 · HTML: https://mlsanity.com/paper/2108.11071/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 14 references that are in the map.
- First posted on arXiv 25 Aug 2021.

## Builds on (most cited first, 5 of 5)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Federated Optimization: Distributed Machine Learning for On-Device Intelligence](https://mlsanity.com/paper/1610.02527/) (2016)
- [Anytime MiniBatch: Exploiting Stragglers in Online Distributed Optimization](https://mlsanity.com/paper/2006.05752/) (2020)
- [Efficient Distributed Online Prediction and Stochastic Optimization with Approximate Distributed Averaging](https://mlsanity.com/paper/1403.0603/) (2014)

## Built on by (most cited first, 1 of 1)

- [Asynchronous Decentralized Learning over Unreliable Wireless Networks](https://mlsanity.com/paper/2202.00955/) (2022)

## Abstract (arXiv)

We consider decentralized consensus optimization when workers sample data from non-identical distributions and perform variable amounts of work due to slow nodes known as stragglers. The problem of non-identical distributions and the problem of variable amount of work have been previously studied separately. In our work we analyze them together under a unified system model. We study the convergence of the optimization algorithm when combining worker outputs under two heuristic methods: (1) weighting equally, and (2) weighting by the amount of work completed by each. We prove convergence of the two methods under perfect consensus, assuming straggler statistics are independent and identical across all workers for all iterations. Our numerical results show that under approximate consensus the second method outperforms the first method for both convex and non-convex objective functions. We make use of the theory on minimum variance unbiased estimator (MVUE) to evaluate the existence of an optimal method for combining worker outputs. While we conclude that neither of the two heuristic methods are optimal, we also show that an optimal method does not exist.