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Multi-armed bandit algorithms have been argued for decades as useful foradaptively randomized experiments. In such experiments, an algorithm varieswhich arms (e.g. alternative interventions to help students learn) are assignedto participants, with the goal of assigning higher-reward arms to as manyparticipants as possible. We applied the bandit algorithm Thompson Sampling(TS) to run adaptive experiments in three university classes. Instructors sawgreat value in trying to rapidly use data to give their students in theexperiments better arms (e.g. better explanations of a concept). Ourdeployment, however, illustrated a major barrier for scientists andpractitioners to use such adaptive experiments: a lack of quantifiable insightinto how much statistical analysis of specific real-world experiments isimpacted (Pallmann et al, 2018; FDA, 2019), compared to traditional uniformrandom assignment. We therefore use our case study of the ubiquitous two-armbinary reward setting to empirically investigate the impact of using ThompsonSampling instead of uniform random assignment. In this setting, using commonstatistical hypothesis tests, we show that collecting data with TS can as muchas double the False Positive Rate (FPR; incorrectly reporting differences whennone exist) and the False Negative Rate (FNR; failing to report differenceswhen they exist)...

Challenges in Statistical Analysis of Data Collected by a Bandit  Algorithm: An Empirical Exploration in Applications to Adaptively Randomized  Experiments