We address the brittleness of Bayesian experimental design under model misspecification by formulating the problem as a max--min game between the experimenter and an adversarial nature subject to information-theoretic constraints. We demonstrate that this approach yields a robust objective governed by Sibson's $α$-mutual information~(MI), which identifies the $α$-tilted posterior as the robust belief update and establishes the Rényi divergence as the appropriate measure of conditional information gain. To mitigate the bias and variance of nested Monte Carlo estimators needed to estimate Sibson's $α$-MI, we adopt a PAC-Bayes framework to search over stochastic design policies, yielding rigorous high-probability lower bounds on the robust expected information gain that explicitly control finite-sample error.

翻译：针对模型误设下贝叶斯实验设计的脆弱性，我们通过将问题建模为实验者与受信息论约束的对抗性自然之间的最大化-极小化博弈来解决该问题。我们证明该方法产生了一个由Sibson $α$-互信息（MI）支配的鲁棒目标函数，该函数将$α$-倾斜后验识别为鲁棒信念更新，并确立Rényi散度为条件信息增益的恰当度量。为减轻估计Sibson $α$-MI所需嵌套蒙特卡洛估计器的偏差与方差，我们采用PAC-Bayes框架对随机设计策略进行搜索，从而为鲁棒期望信息增益提供严格的高概率下界，并显式控制有限样本误差。