Decentralized Federated Learning with Gradient Tracking over Time-Varying Directed Networks
This work addresses the problem of scalable and privacy-preserving machine learning for distributed agents in dynamic networks, representing an incremental improvement over existing methods.
The paper tackles decentralized federated learning over time-varying directed networks by proposing DSGTm-TV, a consensus-based algorithm with gradient tracking and momentum, which achieves linear convergence to the global optimum with exact gradients and converges to a neighborhood with stochastic gradients, enabling agents to use uncoordinated stepsizes and momentum parameters.
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.