Testing Optimality of Sequential Decision-Making
This provides a tool for evaluating optimality in sequential decision-making systems, which is incremental as it builds on existing fluctuation relations for decision time distributions.
The paper tackles the problem of verifying optimality in binary sequential hypothesis testing by introducing a statistical method that tests if a system minimizes average decision times while meeting reliability constraints, using only decision times, outcomes, and true hypotheses without requiring observation statistics or system details, and demonstrates its application through numerical experiments.
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.