2025/04/28 by Shubhada Agrawal, Aaditya Ramdas, Agrawal, Shubhada +1 · 1 citation
Decision Sciences · Engineering · #Advanced Statistical Process Monitoring #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Probability and Risk Models #Statistics Theory (math.ST) #Wireless Communication Security Techniques
paper · pdf · doi:10.48550/arxiv.2504.19952
openalex publication_date 2025/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove two lower bounds for stopping times of sequential tests between general composite nulls and alternatives. The first lower bound is for the setting where the type-1 error level α approaches zero, and equals log(1/α) divided by a certain infimum KL divergence, termed \operatornameKLinf. The second lower bound applies to the setting where α is fixed and \operatornameKLinf approaches 0 (meaning that the null and alternative sets are not separated) and equals c \operatornameKLinf-1 log log \operatornameKLinf-1 for a universal constant c > 0. We also provide a sufficient condition for matching the upper bounds and show that this condition is met in several special cases. Given past work, these upper and lower bounds are unsurprising in their form; our main contribution is the generality in which they hold, for example, not requiring reference measures or compactness of the classes.