# Optimal experimental design: Formulations and computations

arXiv: https://arxiv.org/abs/2407.16212 · HTML: https://mlsanity.com/paper/2407.16212/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jul 2024.

## Built on by (most cited first, 30 of 45)

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- [Recursive Nested Filtering for Efficient Amortized Bayesian Experimental Design](https://mlsanity.com/paper/2409.05354/) (2024)
- [Performance Comparisons of Reinforcement Learning Algorithms for Sequential Experimental Design](https://mlsanity.com/paper/2503.05905/) (2025)
- [Learning where to learn: Training data distribution optimization for scientific machine learning](https://mlsanity.com/paper/2505.21626/) (2025)
- [A Geometric Approach to Optimal Experimental Design](https://mlsanity.com/paper/2510.14848/) (2025)
- [A Likelihood-Free Approach to Goal-Oriented Bayesian Optimal Experimental Design](https://mlsanity.com/paper/2408.09582/) (2024)
- [Bayesian Experimental Design for Model Discrepancy Calibration: An Auto-Differentiable Ensemble Kalman Inversion Approach](https://mlsanity.com/paper/2504.20319/) (2025)
- [Representative, Informative, and De-Amplifying: Requirements for Robust Bayesian Active Learning under Model Misspecification](https://mlsanity.com/paper/2506.07805/) (2025)
- [Goal-Oriented Sequential Bayesian Experimental Design for Causal Learning](https://mlsanity.com/paper/2507.07359/) (2025)
- [Accelerated Learning on Large Scale Screens using Generative Library Models](https://mlsanity.com/paper/2510.16612/) (2025)
- [Dynamic Angle Selection in X-Ray CT: A Reinforcement Learning Approach to Optimal Stopping](https://mlsanity.com/paper/2503.12688/) (2025)
- [One-shot acceleration of transient PDE solvers via online-learned preconditioners](https://mlsanity.com/paper/2509.08765/) (2025)
- [Online Bayesian Experimental Design for Partially Observed Dynamical Systems](https://mlsanity.com/paper/2511.04403/) (2025)
- [Optimal Experimental Design for Reliable Learning of History-Dependent Constitutive Laws](https://mlsanity.com/paper/2603.12365/) (2026)
- [Maximin Robust Bayesian Experimental Design](https://mlsanity.com/paper/2603.14094/) (2026)
- [Metric Match: A Subset Selection Approach to Evaluating LLM Judge Reliability](https://mlsanity.com/paper/2606.15029/) (2026)
- [Bayesian Experimental Design via Score Matching](https://mlsanity.com/paper/2607.08335/) (2026)
- [Green LIME: Improving AI Explainability through Design of Experiments](https://mlsanity.com/paper/2502.12753/) (2025)
- [Gradient-Free Sequential Bayesian Experimental Design via Interacting Particle Systems](https://mlsanity.com/paper/2504.13320/) (2025)

## Abstract (arXiv)

Questions of `how best to acquire data' are essential to modeling and prediction in the natural and social sciences, engineering applications, and beyond. Optimal experimental design (OED) formalizes these questions and creates computational methods to answer them. This article presents a systematic survey of modern OED, from its foundations in classical design theory to current research involving OED for complex models. We begin by reviewing criteria used to formulate an OED problem and thus to encode the goal of performing an experiment. We emphasize the flexibility of the Bayesian and decision-theoretic approach, which encompasses information-based criteria that are well-suited to nonlinear and non-Gaussian statistical models. We then discuss methods for estimating or bounding the values of these design criteria; this endeavor can be quite challenging due to strong nonlinearities, high parameter dimension, large per-sample costs, or settings where the model is implicit. A complementary set of computational issues involves optimization methods used to find a design; we discuss such methods in the discrete (combinatorial) setting of observation selection and in settings where an exact design can be continuously parameterized. Finally we present emerging methods for sequential OED that build non-myopic design policies, rather than explicit designs; these methods naturally adapt to the outcomes of past experiments in proposing new experiments, while seeking coordination among all experiments to be performed. Throughout, we highlight important open questions and challenges.