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

2026-06-22

AI Summary

This work addresses a fundamental limitation in conventional Bayesian experimental design, which relies on prior-to-posterior uncertainty reduction and yields an intractable objective that is doubly hard to evaluate and poorly aligned with downstream tasks. By reframing the problem through decision theory, the authors formulate it as optimizing the expected future loss (EFL) of downstream actions, thereby reducing the objective to a singly intractable form that obviates explicit posterior or marginal likelihood computation. They introduce a stochastic gradient method that jointly optimizes both the experimental design and the action policy, requiring only samples from the joint parameter–data model and evaluations of the loss function. This approach naturally accommodates implicit modeling and task-specific customization, demonstrating marked improvements over existing methods in both optimization efficiency and task adaptability.

Abstract

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.

Problem

• Bayesian experimental design
• doubly intractable objectives
• task-driven design
• expected future loss
• downstream tasks

Innovation

• Bayesian experimental design
• expected future loss
• singly intractable objective
• task-driven
• stochastic gradient optimization