A1713
Title: Safe anytime-valid optimal policy recommendation
Authors: Kohei Izumi - University of Rochester (United States) [presenting]
Keita Sunada - University of Rochester (United States)
Abstract: Treatment choice under partial identification has largely been studied in static settings. The sequential version is studied: evidence arrives over time from heterogeneous populations, the planner may stop at any data-dependent time, and the false-recommendation probability must be controlled uniformly over all stopping times. This anytime-valid safety requirement is imposed as a constraint on the policy class. An e-process threshold then defines an admissible class of policies within which the planner minimizes conditional Gamma-minimax regret over a time-consistent (or rectangular) ambiguity set for future evidence. The resulting constrained optimal stopping problem admits a dynamically consistent Bellman equation, and a finite-horizon calibration of the e-process threshold preserves size control while tightening the Ville bound. The analysis recovers, in this dynamic setting, the Type I and II regret asymmetry documented for hypothesis-testing rules in static treatment choice: the welfare cost of anytime-valid safety arises almost entirely as Type II regret---failure to recommend effective treatments---and peaks at moderate positive treatment effects. Relaxing the significance level, calibrating the threshold, and using a data-driven ambiguity set can each mitigate this cost. Two COVID-19 vaccine applications---the BNT162b2 primary series and an mRNA booster against Omicron---illustrate how the framework distinguishes overwhelming from ambiguous evidence.
