Optimal Testing in the Experiment-rich Regime

TL;DR

This paper introduces an optimal experimentation framework for the experiment-rich regime, where numerous hypotheses are tested with costly observations, providing algorithms and heuristics to improve efficiency over traditional methods.

Contribution

It characterizes the optimal policy for experiment selection in the experiment-rich regime and offers a practical algorithm and heuristic for implementation.

Findings

Optimal policy fully characterized and computable.

Heuristic provides intuition and performs well.

High-powered classical tests can be inefficient in this setting.

Abstract

Motivated by the widespread adoption of large-scale A/B testing in industry, we propose a new experimentation framework for the setting where potential experiments are abundant (i.e., many hypotheses are available to test), and observations are costly; we refer to this as the experiment-rich regime. Such scenarios require the experimenter to internalize the opportunity cost of assigning a sample to a particular experiment. We fully characterize the optimal policy and give an algorithm to compute it. Furthermore, we develop a simple heuristic that also provides intuition for the optimal policy. We use simulations based on real data to compare both the optimal algorithm and the heuristic to other natural alternative experimental design frameworks. In particular, we discuss the paradox of power: high-powered classical tests can lead to highly inefficient sampling in the experiment-rich regime.