Optimal Conditional Inference in Adaptive Experiments

TL;DR

This paper develops optimal methods for conditional inference in adaptive batched bandit experiments, accounting for various adaptive choices and invariance properties, with practical procedures for complex scenarios.

Contribution

It introduces optimal conditional inference procedures for adaptive experiments, including cases with location-invariance and polyhedral data dependence, enhancing statistical validity.

Findings

Inference based only on the last batch is optimal without restrictions.

Additional information is available when experiment parameters are location-invariant.

Tractable, optimal procedures are derived for polyhedral-dependent adaptive experiments.

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.