Decentralized Federated Learning with Gradient Tracking over Time-Varying Directed Networks

TL;DR

This paper introduces DSGTm-TV, a decentralized federated learning algorithm that uses gradient tracking and momentum to achieve efficient, privacy-preserving optimization over dynamic directed networks, with proven convergence guarantees.

Contribution

The paper proposes a novel consensus-based algorithm for decentralized federated learning that handles time-varying directed graphs and uncoordinated hyper-parameters, with rigorous convergence analysis.

Findings

Linear convergence to the global optimum with exact gradients.

Convergence in expectation to a neighborhood with stochastic gradients.

Effective performance demonstrated on image and language tasks.

Abstract

We investigate the problem of agent-to-agent interaction in decentralized (federated) learning over time-varying directed graphs, and, in doing so, propose a consensus-based algorithm called DSGTm-TV. The proposed algorithm incorporates gradient tracking and heavy-ball momentum to distributively optimize a global objective function, while preserving local data privacy. Under DSGTm-TV, agents will update local model parameters and gradient estimates using information exchange with neighboring agents enabled through row- and column-stochastic mixing matrices, which we show guarantee both consensus and optimality. Our analysis establishes that DSGTm-TV exhibits linear convergence to the exact global optimum when exact gradient information is available, and converges in expectation to a neighborhood of the global optimum when employing stochastic gradients. Moreover, in contrast to existing methods, DSGTm-TV preserves convergence for networks with uncoordinated stepsizes and momentum parameters, for which we provide explicit bounds. These results enable agents to operate in a fully decentralized manner, independently optimizing their local hyper-parameters. We demonstrate the efficacy of our approach via comparisons with state-of-the-art baselines on real-world image classification and natural language processing tasks.