# Decentralized Federated Averaging via Random Walk

## TL;DR

This paper introduces a decentralized federated averaging method using random walk updates, improving convergence and accuracy in heterogeneous data environments without relying on a central server.

## Contribution

It proposes a novel decentralized federated averaging via random walk (DFedRW), including a quantized version, with theoretical convergence guarantees and superior empirical performance.

## Key findings

- Achieves convergence rate of order O(1/k^{1-q}) under convex conditions.
- Outperforms FedAvg in convergence rate and accuracy.
- Increases test accuracy by over 37% in heterogeneous settings.

## Abstract

Federated Learning (FL) is a communication-efficient distributed machine learning method that allows multiple devices to collaboratively train models without sharing raw data. FL can be categorized into centralized and decentralized paradigms. The centralized paradigm relies on a central server to aggregate local models, potentially resulting in single points of failure, communication bottlenecks, and exposure of model parameters. In contrast, the decentralized paradigm, which does not require a central server, provides improved robustness and privacy. The essence of federated learning lies in leveraging multiple local updates for efficient communication. However, this approach may result in slower convergence or even convergence to suboptimal models in the presence of heterogeneous and imbalanced data. To address this challenge, we study decentralized federated averaging via random walk (DFedRW), which replaces multiple local update steps on a single device with random walk updates. Traditional Federated Averaging (FedAvg) and its decentralized versions commonly ignore stragglers, which reduces the amount of training data and introduces sampling bias. Therefore, we allow DFedRW to aggregate partial random walk updates, ensuring that each computation contributes to the model update. To further improve communication efficiency, we also propose a quantized version of DFedRW. We demonstrate that (quantized) DFedRW achieves convergence upper bound of order $\mathcal{O}(\frac{1}{k^{1-q}})$ under convex conditions. Furthermore, we propose a sufficient condition that reveals when quantization balances communication and convergence. Numerical analysis indicates that our proposed algorithms outperform (decentralized) FedAvg in both convergence rate and accuracy, achieving a 38.3\% and 37.5\% increase in test accuracy under high levels of heterogeneities.