# Expected Gain-based Escalation in Vertical Federated Learning

arXiv: https://arxiv.org/abs/2606.31331 · HTML: https://mlsanity.com/paper/2606.31331/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 17 references that are in the map.
- First posted on arXiv 30 Jun 2026.

## Builds on (most cited first, 11 of 11)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Consistent Estimators for Learning to Defer to an Expert](https://mlsanity.com/paper/2006.01862/) (2020)
- [Predict Responsibly: Improving Fairness and Accuracy by Learning to Defer](https://mlsanity.com/paper/1711.06664/) (2017)
- [Machine Learning with a Reject Option: A survey](https://mlsanity.com/paper/2107.11277/) (2021)
- [Optimal strategies for reject option classifiers](https://mlsanity.com/paper/2101.12523/) (2021)
- [When Does Confidence-Based Cascade Deferral Suffice?](https://mlsanity.com/paper/2307.02764/) (2023)
- [Vertical Federated Learning: A Structured Literature Review](https://mlsanity.com/paper/2212.00622/) (2022)
- [LESS-VFL: Communication-Efficient Feature Selection for Vertical Federated Learning](https://mlsanity.com/paper/2305.02219/) (2023)
- [Communication-Efficient Vertical Federated Learning with Limited Overlapping Samples](https://mlsanity.com/paper/2303.16270/) (2023)

## Abstract (arXiv)

Collaborative inference can improve predictive performance by integrating complementary information across agents, but applying collaborative fusion to every sample can incur unnecessary communication and computational overhead. This trade-off is particularly relevant in vertical federated learning (VFL), where clients observe different views of the same sample and fusion typically requires transmitting intermediate representations to a server. We study selective escalation in a two-round VFL inference protocol, in which a low-cost first round produces a prediction from client posteriors and a second embedding-fusion round is invoked only when it is expected to improve the final decision. We formulate routing as expected-gain score estimation: a sample is escalated when a predicted improvement in correctness justifies the additional communication. The proposed analytical score combines a calibrated pooled posterior with classwise reliability estimates of the VFL model, both obtained from held-out calibration data, yielding an interpretable router that requires no separately trained routing network. Experiments on multi-view classification benchmarks, including controlled test--time view degradation settings, show that the proposed router improves the communication-accuracy trade-off over confidence-, learned-gain-, and deferral-based baselines.