Distributed Experimental Design: Bayes-optimal Fusion of Local Designs

2026-06-16

AI Summary

This work addresses a fundamental limitation in distributed Bayesian experimental design, where local nodes evaluate experiments using only local information, leaving the fusion center without access to global likelihoods or information gains. The paper proposes the first Bayesian optimal fusion rule: local agents submit design decisions based on expected information gain as their utility function, and the fusion center selects the experiment maximizing the conditional expectation of centralized information gain. Departing from conventional classification error criteria, this approach defines loss via information gain regret and establishes corresponding bounds on information loss along with conditions for asymptotic equivalence to the centralized optimum. Numerical experiments demonstrate that the proposed rule closely approximates the performance of an ideal centralized design and significantly outperforms heuristic strategies such as majority voting.

Abstract

We develop a decision-theoretic framework for distributed Bayesian experimental design in which local agents evaluate candidate experiments using expected information gain and transmit their local design decisions to a fusion center. Unlike centralized Bayesian design, where all likelihood components and information-gain values are available to a single planner, the fusion center in the distributed setting chooses a global experiment from compressed local recommendations. We derive the Bayes-optimal fusion rule, which selects the experiment with largest conditional expected centralized information gain given the observed local design decisions. This rule is analogous in spirit to optimal fusion rules in distributed detection, but differs fundamentally because the underlying utility is expected information gain and the resulting loss is information-gain regret rather than classification error. We also establish information-loss bounds and identify conditions under which the decision-only fusion rule is asymptotically equivalent to the centralized design. Numerical experiments show that Bayes-optimal fusion closely approximates the centralized oracle, whereas majority voting can be highly suboptimal when a minority of sites carry disproportionate information.

Problem

• distributed experimental design
• Bayesian experimental design
• information gain
• fusion center
• decision fusion

Innovation

• Bayesian experimental design
• distributed fusion
• information gain
• Bayes-optimal decision
• decision-theoretic framework