Adaptive Experimental Design
Designing experiments that use what they have already learned — to estimate an effect precisely, or to choose the right policy, with fewer units.
- adaptive experiments
- semiparametric efficiency
- policy learning
- ATE
The question
A fixed randomized design commits to an allocation before any data exist. But an experiment produces information as it runs: which arms are noisy, which covariate strata are informative, which comparisons are already settled. An adaptive design feeds that information back into the allocation.
The theoretical questions are how much can be gained, what the limit of the gain is, and whether a sequentially estimated design can attain that limit. The answers depend on what the experiment is for: estimating an average treatment effect precisely is a different objective from choosing the best policy, and the optimal designs differ accordingly.
Designing for estimation
The classical target is the semiparametric efficiency bound for the average treatment effect, and the classical design variable is the propensity score. Active adaptive experimental design (ICML 2024, oral) adds a second design variable — the covariate density, i.e. which units to enroll — and shows that optimizing both lowers the bound strictly further than optimizing the propensity score alone, with an estimator that attains the minimized bound.
Related work develops efficient adaptive designs for ATE estimation (arXiv:2002.05308, revise and resubmit at JASA) and studies the adaptive doubly robust estimator for policy evaluation in adaptive experiments, where the sequential dependence of the data breaks standard asymptotics.
Designing for decisions
When the deliverable is a rule rather than an estimate, the criterion changes to regret. Adaptive Sampling-Policy Learning targets worst-case expected simple regret for a context-dependent policy and is minimax rate-optimal for it. The allocation this criterion recommends is not the one that minimizes estimation variance.
The design of experiments for choosing among treatments connects directly to best-arm identification and to the econometric treatment-choice literature; that side of the work is collected under best-arm identification and treatment choice.
Where it applies
The gains are worth having exactly when observations are expensive and outcomes arrive fast enough to inform later rounds: advertising and marketing experiments, clinical studies with designed enrollment, and policy pilots where the sample is small by construction.