Halt before Deviate! Adaptive Local Effort in Federated Learning

The number of local steps is an important control knob in federated learning, shaping both communication cost and the optimization trajectory. However, heterogeneous data can cause local updates to drift and hinder global progress. Choosing when to stop local training is therefore essential to balance communication efficiency and optimization progress. We propose an adaptive stopping rule that selects each client's local step count by comparing both the direction and magnitude of its average update with a reference formed early in the round. Our analysis explains how the rule responds to differences in local curvature and relates local alignment to global descent. Under a common budget of local updates, the proposed rule achieves comparable accuracy with fewer communication rounds.