Bayesian experimental design (BED) chooses the next experiment, trial allocation, or measurement by estimating which option will reveal the most about an unknown parameter. Its recommendations depend on a simulator, the probabilistic model that predicts outcomes under each design. The NeurIPS 2026 paper, Maximin Robust Bayesian Experimental Design, develops a maximin framework for cases where that simulator is misspecified. The derivation yields a robust information objective, a tempered posterior update, and a PAC-Bayes method for optimizing designs from noisy Monte Carlo estimates.
Nominal information can mislead
Classical BED scores a design ξ with expected information gain (EIG), the mutual information between latent parameters θ and a hypothetical outcome y:
EIG(ξ) = E[log p(y | θ, ξ) - log p(y | ξ)]Misspecification affects both terms. The assumed likelihood determines the posterior update and the predictive distribution over outcomes used to average the gain. A design optimized under the wrong likelihood can therefore produce overconfident posteriors, poor parameter estimates, or low-value measurements.
Earlier robust BED methods have used Gibbs posteriors or hand-selected surrogate distributions. Those techniques can improve robustness, but they may treat data generation and belief updating separately. The paper derives both from one optimization problem.
Nature enters the design loop
The authors formulate robust design as a Stackelberg game with three steps:
- The experimenter commits to a stochastic policy π over candidate designs.
- An adversarial “nature” chooses a joint distribution over parameters and outcomes.
- The experimenter maximizes the minimum information gain under that distribution.
Nature must remain inside a Kullback-Leibler ambiguity ball of radius