# Variational Bayesian Optimal Experimental Design

arXiv: https://arxiv.org/abs/1903.05480 · HTML: https://mlsanity.com/paper/1903.05480/

## Key facts

- Cited by 116 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2019.

## Built on by (most cited first, 30 of 116)

- [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)
- [GFlowNets for AI-Driven Scientific Discovery](https://mlsanity.com/paper/2302.00615/) (2023)
- [Prediction-Oriented Bayesian Active Learning](https://mlsanity.com/paper/2304.08151/) (2023)
- [Implicit Deep Adaptive Design: Policy-Based Experimental Design without Likelihoods](https://mlsanity.com/paper/2111.02329/) (2021)
- [Interventions, Where and How? Experimental Design for Causal Models at Scale](https://mlsanity.com/paper/2203.02016/) (2022)
- [OpenBox: A Generalized Black-box Optimization Service](https://mlsanity.com/paper/2106.00421/) (2021)
- [Optimizing Sequential Experimental Design with Deep Reinforcement Learning](https://mlsanity.com/paper/2202.00821/) (2022)
- [Bayesian Preference Elicitation with Language Models](https://mlsanity.com/paper/2403.05534/) (2024)
- [Bayesian Algorithm Execution: Estimating Computable Properties of Black-box Functions Using Mutual Information](https://mlsanity.com/paper/2104.09460/) (2021)
- [Gradient-based Bayesian Experimental Design for Implicit Models using Mutual Information Lower Bounds](https://mlsanity.com/paper/2105.04379/) (2021)
- [Bayesian Sequential Optimal Experimental Design for Nonlinear Models Using Policy Gradient Reinforcement Learning](https://mlsanity.com/paper/2110.15335/) (2021)
- [Test Distribution-Aware Active Learning: A Principled Approach Against Distribution Shift and Outliers](https://mlsanity.com/paper/2106.11719/) (2021)
- [Amortized Bayesian Experimental Design for Decision-Making](https://mlsanity.com/paper/2411.02064/) (2024)
- [Tight Mutual Information Estimation With Contrastive Fenchel-Legendre Optimization](https://mlsanity.com/paper/2107.01131/) (2021)
- [BoxingGym: Benchmarking Progress in Automated Experimental Design and Model Discovery](https://mlsanity.com/paper/2501.01540/) (2025)
- [Policy-Based Bayesian Experimental Design for Non-Differentiable Implicit Models](https://mlsanity.com/paper/2203.04272/) (2022)
- [Differentiable Multi-Target Causal Bayesian Experimental Design](https://mlsanity.com/paper/2302.10607/) (2023)
- [Active Learning in Bayesian Neural Networks with Balanced Entropy Learning Principle](https://mlsanity.com/paper/2105.14559/) (2021)
- [Are Large Language Models Reliable AI Scientists? Assessing Reverse-Engineering of Black-Box Systems](https://mlsanity.com/paper/2505.17968/) (2025)
- [Variational Bayesian Optimal Experimental Design with Normalizing Flows](https://mlsanity.com/paper/2404.13056/) (2024)
- [Targeted Active Learning for Bayesian Decision-Making](https://mlsanity.com/paper/2106.04193/) (2021)
- [Robust Expected Information Gain for Optimal Bayesian Experimental Design Using Ambiguity Sets](https://mlsanity.com/paper/2205.09914/) (2022)
- [Illusory Attacks: Information-Theoretic Detectability Matters in Adversarial Attacks](https://mlsanity.com/paper/2207.10170/) (2022)
- [Step-DAD: Semi-Amortized Policy-Based Bayesian Experimental Design](https://mlsanity.com/paper/2507.14057/) (2025)
- [Bayesian model calibration for block copolymer self-assembly: Likelihood-free inference and expected information gain computation via measure transport](https://mlsanity.com/paper/2206.11343/) (2022)
- [Enhanced Multimodal Representation Learning with Cross-modal KD](https://mlsanity.com/paper/2306.07646/) (2023)
- [Bayesian Experimental Design via Contrastive Diffusions](https://mlsanity.com/paper/2410.11826/) (2024)
- [Scalable First-Order Bayesian Optimization via Structured Automatic Differentiation](https://mlsanity.com/paper/2206.08366/) (2022)
- [Active Exploration for Robotic Manipulation](https://mlsanity.com/paper/2210.12806/) (2022)

## Abstract (arXiv)

Bayesian optimal experimental design (BOED) is a principled framework for making efficient use of limited experimental resources. Unfortunately, its applicability is hampered by the difficulty of obtaining accurate estimates of the expected information gain (EIG) of an experiment. To address this, we introduce several classes of fast EIG estimators by building on ideas from amortized variational inference. We show theoretically and empirically that these estimators can provide significant gains in speed and accuracy over previous approaches. We further demonstrate the practicality of our approach on a number of end-to-end experiments.