# Action-BED: Task-Driven Bayesian Experimental Design with Singly Intractable Objectives

arXiv: https://arxiv.org/abs/2606.23662 · HTML: https://mlsanity.com/paper/2606.23662/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 69 references that are in the map.
- First posted on arXiv 22 Jun 2026.

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

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [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)
- [Bayesian Experimental Design via Contrastive Diffusions](https://mlsanity.com/paper/2410.11826/) (2024)
- [Goal-Oriented Bayesian Optimal Experimental Design for Nonlinear Models using Markov Chain Monte Carlo](https://mlsanity.com/paper/2403.18072/) (2024)
- [Reinforcement Learning: An Overview](https://mlsanity.com/paper/2412.05265/) (2024)
- [JADAI: Jointly Amortizing Adaptive Design and Bayesian Inference](https://mlsanity.com/paper/2512.22999/) (2025)
- [A Geometric Approach to Optimal Experimental Design](https://mlsanity.com/paper/2510.14848/) (2025)
- [Goal-Oriented Sequential Bayesian Experimental Design for Causal Learning](https://mlsanity.com/paper/2507.07359/) (2025)
- [Loss-Driven Bayesian Active Learning](https://mlsanity.com/paper/2604.11995/) (2026)
- [A Multi-fidelity Estimator of the Expected Information Gain for Bayesian Optimal Experimental Design](https://mlsanity.com/paper/2501.10845/) (2025)

## Built on by (most cited first, 2 of 2)

- [Deep adaptive design with an evidential bias criterion](https://mlsanity.com/paper/2608.16466/) (2026)
- [Beyond "AI Helps Humans": Decision-Targeted Evaluation Design for Human-Agent Teams in the Agentic Era](https://mlsanity.com/paper/2609.05527/) (2026)

## Abstract (arXiv)

Bayesian experimental design (BED) has traditionally been based on maximising expected uncertainty reductions from prior to posterior. A major shortfall of this approach is that it leads to doubly intractable objectives that are difficult to optimise, while customising them to particular downstream tasks of interest can also be difficult. Following first principles decision theory, we demonstrate that BED can alternatively be formulated in terms of an expected future loss (EFL) on downstream actions, providing a simple and naturally task-driven framework. Critically, we then show that all such EFLs can be rearranged into singly intractable objectives that can be jointly optimised with respect to both the design policy and a downstream action policy using stochastic gradients, an approach we refer to as ACTION-BED. This formulation further sidesteps the need for any explicit posterior or marginal likelihood estimation and is naturally implicit, requiring only the ability to sample from the joint model over model parameters and data, and evaluate the downstream loss function. It thus allows design policies to be learned more effectively, efficiently, and simply than existing methods, while providing easy customisation to different downstream tasks and losses.