Robust and Decision-Focused BOED
Designing experiments that remain useful when priors are imperfect and decisions matter
Goal: design experiments that are useful, not just informative.
Classical BOED maximizes expected information gain. But information gain alone does not answer two practical questions:
- What if the prior is wrong?
- What if only part of the uncertainty matters for the final decision?
This project addresses both issues.
Two complementary directions
| Direction | Question | Method |
|---|---|---|
| Robust EIG | Can the design survive prior misspecification? | Minimax design over an ambiguity set |
| GoBOED | Does the experiment improve the downstream decision? | Decision-focused design with a differentiable optimization layer |
Robustness to Prior Uncertainty
EIG rankings are sensitive to the prior distribution, and sampling-based EIG estimators behave similarly to EIG under a perturbed prior. We propose robust expected information gain (REIG), which replaces the standard EIG objective with a minimax formulation over an ambiguity set of distributions close to the nominal prior in KL-divergence. We show that REIG corresponds to a log-sum-exp stabilization of the samples used to estimate EIG, making it efficient to implement as a drop-in replacement for standard estimators. REIG improves robustness to prior misspecification and also compensates for the variability of under-sampled EIG estimators (Go & Isaac, 2022).
Decision-Focused Design
Even with a well-specified prior, maximizing EIG does not necessarily improve downstream decision quality. Only the parameter directions that govern the constraints of a control problem truly matter. We propose GoBOED (Goal-driven BOED), a framework that couples BOED with a differentiable convex decision layer equipped with plug-in risk functionals. GoBOED directly optimizes experimental designs for a specified downstream decision objective, rather than maximizing information gain alone.
Key takeaways
- REIG provides robustness to prior misspecification with minimal computational overhead over standard EIG estimators
- GoBOED targets the parameter directions that matter for downstream decisions, rather than reducing all uncertainty uniformly
- Near-optimal design windows are substantially wider under GoBOED than under EIG maximization, offering practical flexibility in experiment design