Algorithms for Adaptive Experiments that Trade-off Statistical Analysis with Reward: Combining Uniform Random Assignment and Reward Maximization
Multi-armed bandit algorithms like Thompson Sampling (TS) can be used to conduct adaptive experiments, in which maximizing reward means that data is used to progressively assign participants to more effective arms. Such assignment strategies increase the risk of statistical hypothesis tests identifying a difference between arms when there is not one, and failing to conclude there is a difference in arms when there truly is one. We tackle this by introducing a novel heuristic algorithm, called TS-PostDiff (Posterior Probability of Difference). TS-PostDiff takes a Bayesian approach to mixing TS and Uniform Random (UR): the probability a participant is assigned using UR allocation is the posterior probability that the difference between two arms is 'small' (below a certain threshold), allowing for more UR exploration when there is little or no reward to be gained. We evaluate TS-PostDiff against state-of-the-art strategies. The empirical and simulation results help characterize the trade-offs of these approaches between reward, False Positive Rate (FPR), and statistical power, as well as under which circumstances each is effective. We quantify the advantage of TS-PostDiff in performing well across multiple differences in arm means (effect sizes), showing the benefits of adaptively changing randomization/exploration in TS in a "Statistically Considerate" manner: reducing FPR and increasing statistical power when differences are small or zero and there is less reward to be gained, while exploiting more when differences may be large. This highlights important considerations for future algorithm development and analysis to better balance reward and statistical analysis.
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