发表机构
Sandia National Laboratories; North Carolina State University（桑迪亚国家实验室; 北卡罗来纳州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出风险感知的目标导向贝叶斯最优实验设计框架，通过三层风险组合推广经典准则，并利用可微嵌套求积估计器实现梯度优化，在传感器放置问题中显著优于传统基线。
AI 中文摘要
传统的贝叶斯最优实验设计（OED）选择最能提供模型参数信息的测量。然而，此类测量对于下游预测可能并非最优。目标导向的OED直接针对预测进行优化。然而，现有的目标导向准则对所有预测不确定性的降低同等对待，无法优先考虑罕见的高后果结果。在本文中，我们开发了一个风险感知框架，该框架在三个层面组合风险，每个层面都推广了经典I-最优和G-最优设计的一个要素：后验预测不确定性的偏差度量（推广预测方差）、跨预测域的风险度量（在I-最优平均和G-最优最坏情况选择之间插值）、以及跨数据集的风险度量（推广期望）。我们从风险四边形中的遗憾函数生成每个层面，因此一个三元组指定了实践者的风险偏好。我们将设计放宽为单位单纯形上的连续权重，并构建了一个在设计变量上可微的嵌套求积估计器。这使得能够使用基于梯度的方法求解最优设计问题，避免了候选设计的组合搜索。对于线性高斯对数正态模型和非线性扩展，我们推导了闭式目标。这些提供了精确的参考，我们据此验证估计器的收敛性。我们展示了该框架在由对流扩散方程控制的反问题中寻找最优传感器放置的应用。我们发现风险感知设计显著优于期望信息增益基线，后者在统计上与随机分配无法区分。
英文摘要
Traditional Bayesian optimal experimental design (OED) selects measurements that best inform a model's parameters. However, such measurements can be suboptimal for downstream predictions. Goal-oriented OED targets the prediction directly. However, the existing goal-oriented criteria value all reductions in predictive uncertainty equally, with no way to prioritize rare, high-consequence outcomes. In this article, we develop a risk-aware framework that composes risk at three levels, each generalizing an ingredient of classical $I$- and $G$-optimal design: a deviation measure of the posterior predictive uncertainty (generalizing the predictive variance), a risk measure across the prediction domain (interpolating $I$-optimal averaging and $G$-optimal worst-case selection), and a risk measure over datasets (generalizing the expectation). We generate each level from a regret function in the risk quadrangle, so that one triple specifies a practitioner's risk preference. We relax the design to continuous weights on the unit simplex and construct a nested-quadrature estimator that is differentiable in the design variable. This enables solving the optimal design problem with gradient-based methods, avoiding a combinatorial search over candidate designs. For a linear-Gaussian lognormal model and a nonlinear extension, we derive closed-form objectives. These give exact references against which we verify that the estimator converges. We demonstrate this framework for finding optimal sensor placements in an inverse problem governed by an advection-diffusion equation. We find that the risk-aware designs substantially outperform the expected-information-gain baseline, which is statistically indistinguishable from a random allocation.
