Regret-weighted Bayes Fusion for Distributed Experimental Design

2026-07-12

AI Summary

This work addresses the challenges in distributed experimental design where local sites possess incomplete information and generate heterogeneous, potentially conflicting recommendations. To tackle this, the authors propose a Bayesian fusion method that minimizes expected information regret under the posterior distribution, treating the centralized optimal experiment as an unknown ground-truth label. Instead of conventional majority voting or maximum a posteriori (MAP) estimation, the approach employs information-regret-weighted aggregation, making it suitable for scenarios with asymmetric loss structures. Theoretical analysis demonstrates that majority voting is optimal only under symmetric assumptions, whereas the proposed method remains effective beyond such constraints. Numerical experiments confirm that when labels and regret are misaligned, the method significantly reduces information loss and outperforms baseline strategies such as MAP.

Abstract

We study distributed experimental design with multiple candidate experiments, where local sites possess only partial information and transmit design recommendations to a fusion center. Unlike centralized design, in which the experiment that maximizes expected information gain can be selected directly, distributed design requires combining heterogeneous and potentially conflicting local recommendations. Formulating as a multi-class Bayes fusion problem, centralized oracle design is treated as an unknown label and each site is characterized by a local recommendation mechanism. The proposed fusion rule minimizes posterior expected information regret, rather than merely maximizing the number of local votes or the posterior probability (MAP) of the oracle label. This distinction is essential because different incorrect experimental choices may incur different losses in information gain. We show that majority vote is optimal only under restrictive symmetry assumptions and can otherwise be strictly suboptimal. Regret-weighted multi-class Chernoff bounds are derived to identify the pairwise separations governing distributed design performance. Numerical studies identify two operational regimes: MAP is effective when oracle-label accuracy and information regret are aligned, while regret-weighted Bayes fusion reduces information loss when the most probable oracle label is not the lowest-regret decision.

Problem

• distributed experimental design
• Bayes fusion
• information regret
• multi-class fusion
• oracle design

Innovation

• regret-weighted Bayes fusion
• distributed experimental design
• information regret
• multi-class Chernoff bounds
• Bayesian decision fusion