Testing Optimality of Sequential Decision-Making
Abstract
This paper provides a statistical method to test whether a system that performs a binary sequential hypothesis test is optimal in the sense of minimizing the average decision times while taking decisions with given reliabilities. The proposed method requires samples of the decision times, the decision outcomes, and the true hypotheses, but does not require knowledge on the statistics of the observations or the properties of the decision-making system. The method is based on fluctuation relations for decision time distributions which are proved for sequential probability ratio tests. These relations follow from the martingale property of probability ratios and hold under fairly general conditions. We illustrate these tests with numerical experiments and discuss potential applications.
Cite
@article{arxiv.1801.01574,
title = {Testing Optimality of Sequential Decision-Making},
author = {Meik Dörpinghaus and Izaak Neri and Édgar Roldán and Heinrich Meyr and Frank Jülicher},
journal= {arXiv preprint arXiv:1801.01574},
year = {2018}
}
Comments
42 pages, 7 figures