Robust Bayesian Decision Making under Adversarial Uncertainty

Bayesian optimal experimental design (BOED) selects experiments to maximize information gain about model parameters. However, in decision-critical settings, reducing parameter uncertainty does not necessarily improve downstream decisions, as only specific parameter directions relevant to the objective truly matter. We propose GoBOED, a goal-driven BOED framework that directly optimizes experimental designs for a specified decision-making objective. GoBOED combines an amortized variational posterior surrogate with a differentiable convex decision layer, enabling gradient-based design optimization that is fully decision-focused. We theoretically show that GoBOED gradients are insensitive to parameter directions irrelevant to the decision objective, providing a formal justification for why goal-driven design achieves equivalent decision quality over a wider set of experimental designs than information-gain maximization. Empirically, across source localization, epidemic management, and pharmacokinetic control, GoBOED identifies designs that better align with downstream decision objectives and reveals that near-optimal design windows are substantially wider than those predicted by goal-agnostic BOED approaches.

Online experiments in ads, recommendation, and member-experience systems are often planned before the dominant interference mechanism is known. A treatment may propagate through budgets, inventory, producer exposure, graph spillovers, or temporal carryover, making the randomization design itself a statistical decision. We formulate this problem as robust design selection over uncertain exposure mechanisms. Given a finite catalog of six implementable designs, the selector compares each design by worst-case planning risk over an ambiguity set. The risk combines exposure bias, assignment-unit variance, minimum detectable effect, contamination or carryover, operational cost, and estimand mismatch. For theoretical justification, the paper develops a geometry-aware guarantee, stating that design bias is bounded by Wasserstein distance to the launch exposure distribution, and this penalty is minimax tight under Lipschitz exposure response. We also prove finite-catalog approximation and a robust selector theorem with excess-risk control, exact recovery under separation, and certified shortlists when the risk surface is flat. Empirically, the same selector gives different recommendations across samples from public datasets. It selects user-randomization on Criteo ads with dimensionless robust risk 1.295, switchbacks on Open Bandit-bts/men with risk 2.105, and cluster-randomization on KuaiRand with risk 2.240. The Open Bandit case stresses known but uneven logging support, with propensities from 0.00006 to 0.594 and a 5.17% IPS effective-sample share. Overall, the paper contributes an interference-aware experiment design framework based on mechanism-robust design decisions, where the output is either a justified design choice or an uncertainty shortlist.

Bayesian experimental design (BED) is a principled framework for data-efficient design of sequential experiments. However, existing BED methods are unable to adapt to dynamic constraints inherent in real-world tasks due to budget limitations, varying costs, or physical constraints that restrict how designs evolve over time. In this paper, we introduce a novel approach to BED that enables constrained optimization of experimental designs by combining offline pre-training of an amortized policy and a posterior network with online multi-step lookahead planning using scenario trees. We empirically demonstrate that our method yields substantially more informative design sequences than existing methods across a range of constrained BED tasks, while incurring only a modest additional computational overhead.