CTP-FL: Common-Trajectory Gradient Prediction for Federated Learning

Junkang Liu

Communication-efficient federated optimization commonly spends several gradient evaluations between server updates. Existing local-update methods use this computation to advance an independent model on each client. Under heterogeneous data, however, these models evaluate gradients at different locations, making the aggregated update difficult to interpret as a gradient of the global objective. We study an alternative use of the same computation budget: \emph{evaluate the global objective along a shared, predicted path}. We propose Common-Trajectory Predictive Federated Learning (\texttt{CTP-FL}). At each round, all clients construct the same sequence of query points from the current global model and the previous aggregated direction, evaluate $K$ stochastic gradients along this sequence, and upload their average. The server then performs a single global update. Thus, \texttt{CTP-FL} uses $K$ mini-batch gradients per client and one model-sized vector in each communication direction, matching the per-round computation and communication of full-participation FedAvg-M. Shared query points make the aggregated direction an unbiased estimator of the average \emph{global} gradient along…