用于分布式实验设计的后悔加权贝叶斯融合
Regret-weighted Bayes Fusion for Distributed Experimental Design
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中文总结 AI 辅助
研究分布式实验设计，本地站点信息不全需融合建议。提出后悔加权贝叶斯融合规则，最小化后验期望信息后悔，推导后悔加权多类切尔诺夫界。数值研究表明不同模式下MAP和该融合规则各有优势，可减少信息损失。
中文摘要 AI 辅助
我们研究了具有多个候选实验的分布式实验设计，其中本地站点仅拥有部分信息并将设计建议传输到融合中心。与集中式设计不同，分布式设计需要组合异构且可能冲突的本地建议。我们将其表述为多类贝叶斯融合问题，把集中式神谕设计视为未知标签，每个站点由本地建议机制表征。所提出的融合规则最小化后验期望信息后悔，而非仅仅最大化本地票数或神谕标签的后验概率（MAP）。我们表明多数投票仅在严格对称假设下才是最优的，否则可能严格次优。我们推导了后悔加权多类切尔诺夫界来识别控制分布式设计性能的成对分离。数值研究确定了两种操作模式：当神谕标签准确性和信息后悔一致时，MAP有效；而当最可能的神谕标签不是最低后悔决策时，后悔加权贝叶斯融合减少信息损失。
英文摘要
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.
