Resolution-Aware Experimental Design under Partial Identifiability

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.

Scientific experiments are often designed to maximize information gain, yet in many applications the primary objective is to support reliable downstream decision-making. Existing decision-aware experimental design and active learning methods typically assume well-specified outcome models and implicitly rely on the stability of the optimal decision under real-world perturbations. In practice, however, experimental outcomes are frequently influenced by hidden or weakly modeled effects, which can substantially alter decision optimality and lead to misleading conclusions. We study sequential adversarially robust decision-aware experimental design, where data acquisition has to take into account information gain against plausible worst-case unexpected effects, modeled here as variation in adversarial variables. Building on Bayesian decision theory, we formalize an adversarially robust optimal decision under this setting and derive a principled Bayesian experimental design criterion. The criterion explicitly targets decision stability rather than nominal optimality. Experiments on synthetic and real-world scientific datasets show that conventional decision-aware design can converge rapidly to high confidence yet fragile decisions, while our robustness-aware approach yields decisions that are significantly more stable and reliable under adversarial variation.

Causal queries are often only partially identifiable from observational data, and experiments that could tighten the resulting bounds are typically costly. We study the problem of selecting, prior to observing experimental outcomes, a cost-constrained subset of experiments that maximally tightens bounds on a target query. We formalize this as the max-potency problem, where epistemic potency measures the worst-case reduction in bound width guaranteed by an experiment, and show that this problem is NP-hard via a reduction from 0-1 knapsack. Building on the polynomial-programming framework of Duarte et al. (2023), we give a general procedure for evaluating epistemic potency in discrete settings. To control the super-exponential search space, we introduce two graphical pruning criteria that depend only on the causal graph and the query: a novel path-interception rule that exploits district structure to certify zero potency in linear time, and an identifiability check based on the ID algorithm. On Erdos-Renyi random graphs and 11 bnlearn benchmark networks, the two criteria together prune 50-88% of candidate experiments on average without solving a single polynomial program. For the general subset search, we show that ID-pruned experiments are combinatorially inert, yielding a super-exponential reduction in the number of subsets evaluated. We close with an end-to-end demonstration on observational NHANES data, selecting optimal experiments for estimating the effect of physical activity on diabetes.