对抗性环境下的鲁棒实验设计，用信息论约束提升可靠性
Maximin Robust Bayesian Experimental Design
- 将实验设计建模为对抗博弈，引入Sibson的α-互信息
- α-倾斜后验为鲁棒信念更新，瑞尼散度衡量信息增益
- 结合PAC-Bayes框架，控制有限样本误差
我们通过将问题建模为实验者与对抗性自然之间的最大最小博弈，并施加信息论约束，解决了贝叶斯实验设计在模型误设下的脆弱性问题。该方法导出了由Sibson的α-互信息（MI）支配的鲁棒目标，确定了α-倾斜后验为鲁棒信念更新方式，并确立瑞尼散度为条件信息增益的合适度量。为缓解估计Sibson的α-MI所需的嵌套蒙特卡罗估计器的偏差与方差，我们采用PAC-Bayes框架搜索随机设计策略，从而获得鲁棒期望信息增益的严格高概率下界，显式控制有限样本误差。
原文摘要 · Abstract (English)
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.
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