Maximin Robust Bayesian Experimental Design

• URL: http://arxiv.org/abs/2603.14094v1
• Date: Sat, 14 Mar 2026 19:40:39 GMT
• Title: Maximin Robust Bayesian Experimental Design
• Abstract summary: We address the brittleness of experimental design under model misspecification by formulating the problem as a max--min game between the experimenter and an adversarial nature.<n>We demonstrate that this approach yields a robust objective governed by Sibson's $$-mutual information(MI)<n>To mitigate the bias and variance of nested Monte Carlo estimators needed to estimate Sibson's $$-MI, we adopt a PAC-Bayes framework to search over design policies.
• Score: 10.698592443430323
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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