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Beyond Expected Information Gain: Stable Bayesian Optimal Experimental Design with Integral Probability Metrics and Plug-and-Play Extensions

arXiv 2604.21849 ↗First posted 23 Apr 2026stat.ML cs.LG cs.NAcited by 0

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Abstract (arXiv)

Bayesian Optimal Experimental Design (BOED) provides a rigorous framework for decision-making tasks in which data acquisition is often the critical bottleneck, especially in resource-constrained settings. Traditionally, BOED typically selects designs by maximizing expected information gain (EIG), commonly defined through the Kullback-Leibler (KL) divergence. However, classical evaluation of EIG often involves challenging nested expectations, and even advanced variational methods leave the underlying log-density-ratio objective unchanged. As a result, support mismatch, tail underestimation, and rare-event sensitivity remain intrinsic concerns for KL-based BOED. To address these fundamental bottlenecks, we introduce an IPM-based BOED framework that replaces density-based divergences with integral probability metrics (IPMs), including the Wasserstein distance, Maximum Mean Discrepancy, and Energy Distance, resulting in a highly flexible plug-and-play BOED framework. We establish theoretical guarantees showing that IPM-based utilities provide stronger geometry-aware stability under surrogate-model error and prior misspecification than classical EIG-based utilities. We also validate the proposed framework empirically, demonstrating that IPM-based designs yield highly concentrated credible sets. Furthermore, by extending the same sample-based BOED template in a plug-and-play manner to geometry-aware discrepancies beyond the IPM class, illustrated by a neural optimal transport estimator, we achieve accurate optimal designs in high-dimensional settings where conventional nested Monte Carlo estimators and advanced variational methods fail.

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References · 37

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2023Direct Preference Optimization: Your Language Model is Secretly a Reward Modelcited by 7,916
  3. 2022Flow Matching for Generative Modelingcited by 5,426
  4. 2022Beyond neural scaling laws: beating power law scaling via data pruningcited by 519
  5. 2016Input Convex Neural Networkscited by 407
  6. 2023Data Selection for Language Models via Importance Resamplingcited by 322
  7. 2019Optimal transport mapping via input convex neural networkscited by 202
  8. 2023Modern Bayesian Experimental Designcited by 121
  9. 2019Variational Bayesian Optimal Experimental Designcited by 116
  10. 2021Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Designcited by 103
  11. 2019Wasserstein-2 Generative Networkscited by 96
  12. 2019Sequential Experimental Design for Transductive Linear Banditscited by 88
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  1. 2017On Nesting Monte Carlo Estimatorscited by 82
  2. 2021High-Dimensional Experimental Design and Kernel Banditscited by 55
  3. 2024Active Preference Learning for Large Language Modelscited by 55
  4. 2018Efficient Bayesian Experimental Design for Implicit Modelscited by 34
  5. 2022Instance-Dependent Near-Optimal Policy Identification in Linear MDPs via Online Experiment Designcited by 33
  6. 2021Wasserstein Generative Learning of Conditional Distributioncited by 24
  7. 2024An Experimental Design Framework for Label-Efficient Supervised Finetuning of Large Language Modelscited by 22
  8. 2015On the Computational Complexity of High-Dimensional Bayesian Variable Selectioncited by 18
  9. 2021Adaptive variational Bayes: Optimality, computation and applicationscited by 17
  10. 2014A Fast and Scalable Method for A-Optimal Design of Experiments for Infinite-dimensional Bayesian Nonlinear Inverse Problemscited by 14
  11. 2023Wasserstein Generative Regressioncited by 12
  12. 2025Adaptive Defense against Harmful Fine-Tuning for Large Language Models via Bayesian Data Schedulercited by 12
  13. 2021Edge-promoting adaptive Bayesian experimental design for X-ray imagingcited by 10
  14. 2025Provable Diffusion Posterior Sampling for Bayesian Inversioncited by 8
  15. 2020Optimal design of acoustic metamaterial cloaks under uncertaintycited by 7
  16. 2025Bayesian optimal experimental design with Wasserstein information criteriacited by 7
  17. 2025PINS: Proximal Iterations with Sparse Newton and Sinkhorn for Optimal Transportcited by 5
  18. 2025Balancing Interference and Correlation in Spatial Experimental Designs: A Causal Graph Cut Approachcited by 5
  19. 2022Supervised Optimal Transportcited by 4
  20. 2024Expected information gain estimation via density approximations: Sample allocation and dimension reductioncited by 4
  21. 2013Selection and Estimation for Mixed Graphical Modelscited by 3
  22. 2025A Geometric Approach to Optimal Experimental Designcited by 2
  23. 2024PNOD: An Efficient Projected Newton Framework for Exact Optimal Experimental Designscited by 1
  24. 2025Data selection: at the interface of PDE-based inverse problem and randomized linear algebracited by 1
  25. 2026Observationally Informed Adaptive Causal Experimental Designcited by 1

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