# A Unified Stochastic Gradient Approach to Designing Bayesian-Optimal Experiments

arXiv: https://arxiv.org/abs/1911.00294 · HTML: https://mlsanity.com/paper/1911.00294/

## Key facts

- Cited by 58 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2019.

## Built on by (most cited first, 30 of 58)

- [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)
- [Active Testing: Sample-Efficient Model Evaluation](https://mlsanity.com/paper/2103.05331/) (2021)
- [GFlowNets for AI-Driven Scientific Discovery](https://mlsanity.com/paper/2302.00615/) (2023)
- [Implicit Deep Adaptive Design: Policy-Based Experimental Design without Likelihoods](https://mlsanity.com/paper/2111.02329/) (2021)
- [Investigating the Role of Negatives in Contrastive Representation Learning](https://mlsanity.com/paper/2106.09943/) (2021)
- [Interventions, Where and How? Experimental Design for Causal Models at Scale](https://mlsanity.com/paper/2203.02016/) (2022)
- [Optimizing Sequential Experimental Design with Deep Reinforcement Learning](https://mlsanity.com/paper/2202.00821/) (2022)
- [Decomposed Mutual Information Estimation for Contrastive Representation Learning](https://mlsanity.com/paper/2106.13401/) (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)
- [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)
- [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)
- [Step-DAD: Semi-Amortized Policy-Based Bayesian Experimental Design](https://mlsanity.com/paper/2507.14057/) (2025)
- [Bayesian Experimental Design via Contrastive Diffusions](https://mlsanity.com/paper/2410.11826/) (2024)
- [Probabilistic Bayesian optimal experimental design using conditional normalizing flows](https://mlsanity.com/paper/2402.18337/) (2024)
- [Amortized Active Causal Induction with Deep Reinforcement Learning](https://mlsanity.com/paper/2405.16718/) (2024)
- [Variational Sequential Optimal Experimental Design using Reinforcement Learning](https://mlsanity.com/paper/2306.10430/) (2023)
- [ALINE: Joint Amortization for Bayesian Inference and Active Data Acquisition](https://mlsanity.com/paper/2506.07259/) (2025)
- [A Scalable Gradient-Free Method for Bayesian Experimental Design with Implicit Models](https://mlsanity.com/paper/2103.08026/) (2021)
- [Design Amortization for Bayesian Optimal Experimental Design](https://mlsanity.com/paper/2210.03283/) (2022)
- [Statistically Efficient Bayesian Sequential Experiment Design via Reinforcement Learning with Cross-Entropy Estimators](https://mlsanity.com/paper/2305.18435/) (2023)
- [Bayesian Active Learning in the Presence of Nuisance Parameters](https://mlsanity.com/paper/2310.14968/) (2023)
- [Statistical applications of contrastive learning](https://mlsanity.com/paper/2204.13999/) (2022)
- [On Estimating the Gradient of the Expected Information Gain in Bayesian Experimental Design](https://mlsanity.com/paper/2308.09888/) (2023)
- [PASOA- PArticle baSed Bayesian Optimal Adaptive design](https://mlsanity.com/paper/2402.07160/) (2024)
- [Energy-Based Modelling for Discrete and Mixed Data via Heat Equations on Structured Spaces](https://mlsanity.com/paper/2412.01019/) (2024)

## Abstract (arXiv)

We introduce a fully stochastic gradient based approach to Bayesian optimal experimental design (BOED). Our approach utilizes variational lower bounds on the expected information gain (EIG) of an experiment that can be simultaneously optimized with respect to both the variational and design parameters. This allows the design process to be carried out through a single unified stochastic gradient ascent procedure, in contrast to existing approaches that typically construct a pointwise EIG estimator, before passing this estimator to a separate optimizer. We provide a number of different variational objectives including the novel adaptive contrastive estimation (ACE) bound. Finally, we show that our gradient-based approaches are able to provide effective design optimization in substantially higher dimensional settings than existing approaches.