Peter Frazier, Angela J. Yu
Most models of decision-making in neuroscience assume an inﬁnite horizon, which yields an optimal solution that integrates evidence up to a ﬁxed decision threshold; however, under most experimental as well as naturalistic behavioral settings, the decision has to be made before some ﬁnite deadline, which is often experienced as a stochastic quantity, either due to variable external constraints or internal timing uncertainty. In this work, we formulate this problem as sequential hypothesis testing under a stochastic horizon. We use dynamic programming tools to show that, for a large class of deadline distributions, the Bayes-optimal solution requires integrating evidence up to a threshold that declines monotonically over time. We use numerical simulations to illustrate the optimal policy in the special cases of a ﬁxed deadline and one that is drawn from a gamma distribution.