Diffusion Asymptotics for Sequential Experiments
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We propose a new diffusion-asymptotic analysis for sequentially randomized experiments. Rather than taking sample size n to infinity while keeping the problem parameters fixed, we let the mean signal level scale to the order 1/√(n) so as to preserve the difficulty of the learning task as n gets large. In this regime, we show that the behavior of a class of methods for sequential experimentation converges to a diffusion limit. This connection enables us to make sharp performance predictions and obtain new insights on the behavior of Thompson sampling. Our diffusion asymptotics also help resolve a discrepancy between the Θ(log(n)) regret predicted by the fixed-parameter, large-sample asymptotics on the one hand, and the Θ(√(n)) regret from worst-case, finite-sample analysis on the other, suggesting that it is an appropriate asymptotic regime for understanding practical large-scale sequential experiments.
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