Optimal Conditional Inference in Adaptive Experiments
Jiafeng Chen, Isaiah Andrews
TL;DR
This work addresses inference in batched adaptive experiments by conditioning on the realized experimental design. It shows that, without restrictions, last-batch-only inference is optimal, but for location-invariant designs there is a leftover statistic $L$ from earlier batches that improves conditional inference, culminating in a GLS-type estimator for $\eta'\mu$. When the design is further restricted to polyhedral forms, the authors derive computationally tractable, optimal conditional procedures using a truncated-normal framework. The results are supported by uniform-asymptotic theory and simulation evidence, showing substantial gains in interval tightness while preserving conditional validity. Together, these contributions enhance reliable inference in adaptive experiments and offer practical guidance for pilot studies and polyhedral algorithm settings.
Abstract
We study batched bandit experiments and consider the problem of inference conditional on the realized stopping time, assignment probabilities, and target parameter, where all of these may be chosen adaptively using information up to the last batch of the experiment. Absent further restrictions on the experiment, we show that inference using only the results of the last batch is optimal. When the adaptive aspects of the experiment are known to be location-invariant, in the sense that they are unchanged when we shift all batch-arm means by a constant, we show that there is additional information in the data, captured by one additional linear function of the batch-arm means. In the more restrictive case where the stopping time, assignment probabilities, and target parameter are known to depend on the data only through a collection of polyhedral events, we derive computationally tractable and optimal conditional inference procedures.