
Diffusion Approximations for a Class of Sequential Testing Problems
We consider a decision maker who must choose an action in order to maxim...
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Foundational principles for large scale inference: Illustrations through correlation mining
When can reliable inference be drawn in the "Big Data" context? This pap...
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On the Relationship Between Measures of Relative Efficiency for Random Signal Detection
Relative efficiency (RE), the Pitman asymptotic relative efficiency (ARE...
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A Closer Look at the Worstcase Behavior of Multiarmed Bandit Algorithms
One of the key drivers of complexity in the classical (stochastic) multi...
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Likelihood ratio tests for many groups in high dimensions
In this paper we investigate the asymptotic distribution of likelihood r...
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Predictive Power of Nearest Neighbors Algorithm under Random Perturbation
We consider a data corruption scenario in the classical k Nearest Neighb...
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Diffusion Asymptotics for Sequential Experiments
We propose a new diffusionasymptotic 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 fixedparameter, largesample asymptotics on the one hand, and the Θ(√(n)) regret from worstcase, finitesample analysis on the other, suggesting that it is an appropriate asymptotic regime for understanding practical largescale sequential experiments.
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