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：针对贝叶斯实验设计在模型误设定条件下的脆弱性，我们将该问题建模为实验者与信息论约束下对抗性自然之间的极大极小博弈。研究表明，该方法能导出由Sibson α-互信息控制的稳健目标函数，其中α-倾斜后验被确定为稳健信念更新准则，而Rényi散度则成为衡量条件信息增益的恰当指标。为缓解嵌套蒙特卡洛估计器在估计Sibson α-互信息时产生的偏差与方差，我们采用PAC-贝叶斯框架对随机设计策略进行搜索，从而在严格的高概率下获得稳健期望信息增益的下界，并可显式控制有限样本误差。