AI 中文总结
该研究针对贝叶斯最优实验设计中EIG准则无法控制误导性证据风险的问题，提出BA准则，采用基于策略的深度自适应设计框架优化，在多类实验中验证了BA设计与EIG设计的差异。
AI 中文摘要
贝叶斯最优实验设计（BOED）旨在通过优化反映实验目标的期望效用，收集具有信息价值的数据。然而，对于常见效用函数和复杂模型，这种优化在计算上具有挑战性，对于顺序或自适应设计而言更是如此——在这类设计中，设计与数据收集交替进行，必须考虑已观测数据的反馈。现有大多数BOED研究采用信息增益作为效用函数，即期望信息增益（EIG）准则。尽管EIG应用广泛，但它可能并不总能充分反映实验目标：EIG可被视为平均奖励为真实情况产生大量正面证据的实验，但并未直接控制实验产生误导性证据的风险。本文考虑一种替代准则，即偏差 against（BA），其优先控制此类风险。为解决将该准则应用于自适应设计时的计算挑战，本文采用了一种基于策略的深度自适应设计框架，该框架此前已用于EIG准则。最小化BA目标的可处理上界等价于最大化方差惩罚的EIG准则，本文通过蒙特卡洛近似该准则，并使用随机梯度方法学习设计策略。在包括复杂离散选择实验的自适应设计在内的多个示例中，本文展示了BA设计与EIG设计的差异。
英文摘要
Bayesian optimal experimental design (BOED) aims to collect informative data by optimizing an expected utility reflecting the goals of an experiment. However, this optimization is computationally challenging for common utilities and complex models. This is especially so for sequential or adaptive designs, where design and data collection alternate, so that feedback from already observed data must be taken into account. Most existing BOED research employs information gain as the utility, leading to the expected information gain (EIG) criterion. While EIG is widely useful, it may not always adequately reflect experimental goals. EIG can be viewed as rewarding experiments that produce large positive evidence for the truth on average, but it does not directly control the risk of an experiment producing misleading evidence. Here we consider an alternative criterion, which we call bias against (BA), that prioritizes such control. To address computational challenges when applying this criterion for adaptive design, we consider a policy-based deep adaptive design framework, which has previously been used for the EIG criterion. Minimizing a tractable upper bound on the BA objective is equivalent to maximizing a variance-penalized EIG criterion, and we optimize the latter by approximating it by Monte Carlo and learning design policies using stochastic gradient methods. The differences between BA and EIG designs are demonstrated in several examples including the adaptive design of a complex discrete choice experiment.
Comments54 pages, 12 Figures
