Active Sequential Testing of Means

Presenter

• Name: Aditya Gangrade
• Affiliation: University of Michigan, Electrical Engineering and Computer Science
• Contact: https://adityagangrade.wordpress.com

Details

• Date: Monday, November 20, 2023
• Time: 12:00 PM
• Location: EECS, room 2311

Abstract

Suppose that an experimenter can perform $K$ possible experiments, and upon selecting experiment $k$, they observe an independent 1-subGaussian signal with mean ${\mu }^k$. I will consider testing the composite null hypothesis that for each $k,{\mu }^k\le 0$ (versus $\mathrm{\exists }k:{\mu }^k>0$), in an adaptive setting where the experimenter can look at the results of previous experiments before deciding which one to carry out next, with the overall goal of minimising the total number of experiments to reliably test.

While such ‘active sequential testing’ problems have been extremely well studied ever since Chernoff’s seminal work on then in the ’50s, I will show, via an information theoretic lower bound, that the existing analyses of these problems completely misses the significant dependence of the experimental costs on $K$, the number of possible experiments. I will further describe worst-case optimal schemes based on low-regret bandit algorithms, and a law of iterated logarithms, and present an intriguing conjecture about the low-T behaviour of such methods.

Based on work done jointly with Aditya Gopalan (IISc).

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