Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes

Maximin Robust Bayesian Experimental Design

NeurIPS 2026 · Probabilistic and scientific modeling › Uncertainty and Gaussian processes · approach: Variational Bayesian deep learning · 0 citations (OpenAlex)

Read the paperCheck your idea against 108,967 papers

AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.

Casts Bayesian experimental design under misspecification as a maximin game with KL-constrained adversarial nature, yielding Sibson's alpha-MI as robust expected information gain, alpha-tilted posteriors, and PAC-Bayes stochastic design policies with high-probability lower bounds.

Problem

Bayesian experimental design selects designs by expected information gain, which becomes unreliable under model misspecification; nested Monte Carlo estimates of the objective are also biased and noisy, misleading deterministic optimizers.

Approach

A max-min game between experimenter and adversarial nature with an average KL ambiguity set gives Sibson's alpha-mutual information as the robust objective, with the alpha-tilted posterior as the robust belief update; a PAC-Bayes Gibbs policy over designs handles estimator error with high-probability guarantees.

Key results

• In linear regression at alpha=0.056, optimal robust design gives posterior-mean RMSE 2.47e-1 vs 6.82e-1 for random designs at alpha=1.0 (nominal optimal 2.57e-1).
• PAC-Bayes policy reduces mean regret for linear regression with N=16 from 0.327 (naive) to 0.077 with M=16.
• Nominal posteriors show severe undercoverage; tilted posteriors with alpha<1 move coverage toward or above the diagonal.

Surprising findings

• Nominal expected information gain appears larger in realized histograms, but this is self-referential since it assumes the nominal model is true.

Limitations

• Maximin formulation may yield overly conservative designs.
• Misspecification order alpha must be chosen subjectively and is not calibrated from data.
• Evaluation limited to closed-form toy problems (linear regression and A/B testing).

Experimental setup

Datasets: simulated linear regression (Student-t true process) simulated A/B testing (Beta-Binomial true process)

Benchmarks: linear regression simulation A/B testing simulation

Metrics: realized information gain credible-set coverage posterior-mean RMSE regret relative regret

Baselines: nominal expected information gain (alpha=1) Gibbs expected information gain naive deterministic optimizer

Builds on: Gibbs posteriors Sibson's alpha-mutual information PAC-Bayes nested Monte Carlo expected information gain estimation distributionally robust optimization

Closest papers by meaning

• On Estimating the Gradient of the Expected Information Gain in Bayesian Experimental Design (AAAI 2024 · similarity 0.87)
• PASOA- PArticle baSed Bayesian Optimal Adaptive design (ICML 2024 · similarity 0.86)
• Bayesian Experimental Design Via Contrastive Diffusions (ICLR 2025 · similarity 0.86)
• Nesting Particle Filters for Experimental Design in Dynamical Systems (ICML 2024 · similarity 0.85)
• A Unified Framework for Entropy Search and Expected Improvement in Bayesian Optimization (ICML 2025 · similarity 0.85)
• Uncertainty-based Offline Variational Bayesian Reinforcement Learning for Robustness under Diverse Data Corruptions (NeurIPS 2024 · similarity 0.85)