Decentralized Federated Learning with Gradient Tracking over Time-Varying Directed Networks
<|reference_start|>Decentralized Federated Learning with Gradient Tracking over Time-Varying Directed Networks: 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.<|reference_end|>
@article{nguyen2024decentralized,
    title={Decentralized Federated Learning with Gradient Tracking over
  Time-Varying Directed Networks},
    author={Duong Thuy Anh Nguyen, Su Wang, Duong Tung Nguyen, Angelia Nedich, H.
  Vincent Poor},
    journal={arXiv preprint arXiv:2409.17189},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.17189},
    primaryClass={math.OC cs.LG}
}