# Design Amortization for Bayesian Optimal Experimental Design

arXiv: https://arxiv.org/abs/2210.03283 · HTML: https://mlsanity.com/paper/2210.03283/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 28 references that are in the map.
- First posted on arXiv 7 Oct 2022.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Variational Bayesian Optimal Experimental Design](https://mlsanity.com/paper/1903.05480/) (2019)
- [Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Design](https://mlsanity.com/paper/2103.02438/) (2021)
- [On Nesting Monte Carlo Estimators](https://mlsanity.com/paper/1709.06181/) (2017)
- [A Unified Stochastic Gradient Approach to Designing Bayesian-Optimal Experiments](https://mlsanity.com/paper/1911.00294/) (2019)

## Built on by (most cited first, 7 of 7)

- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [Variational Bayesian Optimal Experimental Design with Normalizing Flows](https://mlsanity.com/paper/2404.13056/) (2024)
- [Probabilistic Bayesian optimal experimental design using conditional normalizing flows](https://mlsanity.com/paper/2402.18337/) (2024)
- [Expected information gain estimation via density approximations: Sample allocation and dimension reduction](https://mlsanity.com/paper/2411.08390/) (2024)
- [From Mice to Trains: Amortized Bayesian Inference on Graph Data](https://mlsanity.com/paper/2601.02241/) (2026)
- [Deep Optimal Sensor Placement for Black Box Stochastic Simulations](https://mlsanity.com/paper/2410.12036/) (2024)
- [Neural Optimal Design of Experiment for Inverse Problems](https://mlsanity.com/paper/2512.23763/) (2025)

## Abstract (arXiv)

Bayesian optimal experimental design is a sub-field of statistics focused on developing methods to make efficient use of experimental resources. Any potential design is evaluated in terms of a utility function, such as the (theoretically well-justified) expected information gain (EIG); unfortunately however, under most circumstances the EIG is intractable to evaluate. In this work we build off of successful variational approaches, which optimize a parameterized variational model with respect to bounds on the EIG. Past work focused on learning a new variational model from scratch for each new design considered. Here we present a novel neural architecture that allows experimenters to optimize a single variational model that can estimate the EIG for potentially infinitely many designs. To further improve computational efficiency, we also propose to train the variational model on a significantly cheaper-to-evaluate lower bound, and show empirically that the resulting model provides an excellent guide for more accurate, but expensive to evaluate bounds on the EIG. We demonstrate the effectiveness of our technique on generalized linear models, a class of statistical models that is widely used in the analysis of controlled experiments. Experiments show that our method is able to greatly improve accuracy over existing approximation strategies, and achieve these results with far better sample efficiency.