# Maximin Robust Bayesian Experimental Design

arXiv: https://arxiv.org/abs/2603.14094 · HTML: https://mlsanity.com/paper/2603.14094/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 64 references that are in the map.
- First posted on arXiv 14 Mar 2026.

## Builds on (most cited first, 22 of 22)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Design](https://mlsanity.com/paper/2103.02438/) (2021)
- [Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It](https://mlsanity.com/paper/1412.3730/) (2014)
- [On Nesting Monte Carlo Estimators](https://mlsanity.com/paper/1709.06181/) (2017)
- [Assigning a value to a power likelihood in a general Bayesian model](https://mlsanity.com/paper/1701.08515/) (2017)
- [Optimizing Sequential Experimental Design with Deep Reinforcement Learning](https://mlsanity.com/paper/2202.00821/) (2022)
- [Optimal experimental design: Formulations and computations](https://mlsanity.com/paper/2407.16212/) (2024)
- [Sample Complexity of Sample Average Approximation for Conditional Stochastic Optimization](https://mlsanity.com/paper/1905.11957/) (2019)
- [Robust Expected Information Gain for Optimal Bayesian Experimental Design Using Ambiguity Sets](https://mlsanity.com/paper/2205.09914/) (2022)
- [Nesting Particle Filters for Experimental Design in Dynamical Systems](https://mlsanity.com/paper/2402.07868/) (2024)
- [Approximate Models and Robust Decisions](https://mlsanity.com/paper/1402.6118/) (2014)
- [Receding Horizon Curiosity](https://mlsanity.com/paper/1910.03620/) (2019)
- [Bayesian decision-theoretic design of experiments under an alternative model](https://mlsanity.com/paper/1909.12570/) (2019)
- [PAC-Bayes Bounds for Bandit Problems: A Survey and Experimental Comparison](https://mlsanity.com/paper/2211.16110/) (2022)
- [Metrics for Bayesian Optimal Experiment Design under Model Misspecification](https://mlsanity.com/paper/2304.07949/) (2023)
- [Calibrating generalized predictive distributions](https://mlsanity.com/paper/2107.01688/) (2021)
- [Gibbs optimal design of experiments](https://mlsanity.com/paper/2310.17440/) (2023)
- [Robust Experimental Design via Generalised Bayesian Inference](https://mlsanity.com/paper/2511.07671/) (2025)

## Built on by (most cited first, 1 of 1)

- [Resolution-Aware Experimental Design under Partial Identifiability](https://mlsanity.com/paper/2609.03686/) (2026)

## Abstract (arXiv)

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 R'enyi 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.