Optimize Federated Learning Communication with Expected Gain-based Escalation.

Vertical Federated Learning (VFL) allows multiple parties to collaboratively train models without sharing raw data, but the communication overhead for integrating information across different data views can be substantial. This paper proposes a two-round inference protocol designed to optimize this trade-off. A low-cost initial round generates a prediction, and a more resource-intensive second round, involving embedding fusion, is only triggered if it's predicted to significantly enhance the final decision. The core of the approach is an "expected-gain score" that determines when to escalate a sample to the second round. This score analytically combines calibrated pooled posteriors with class-wise reliability estimates, derived from held-out calibration data, making the routing decision interpretable without needing a separate routing network. Experiments show this router improves the communication-accuracy trade-off over existing baselines.