Hello everyone,

Next Monday (2023/11/20) at noon, Aditya Gangrade will be presenting in EECS room 2311. Please fill out the food form before attending, so we can buy enough pizza for everyone.

If you have research to share, please volunteer to present using this link. Currently, there is no one scheduled for 2023/12/04 (next seminar). As a token of gratitude, presenters get to choose a customized meal from a selection of local restaurants, as listed here.

All seminar info is available on the SPEECS website, and a Google calendar link with dates/times/presenters is can be found here. If you have any questions, you can contact Zongyu Li or me directly, or email speecs.seminar-requests@umich.edu. Suggestions are always welcome :)

Speaker: Aditya Gangrade

Topic: Active Sequential Testing of Means

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 \(\exists k : \mu^k > 0\)), 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). Supplementary link: None

Mirror: http://websites.umich.edu/~speecsseminar/presentations/20231120/

Thanks,

Matt Raymond