Optimal sequential sampling with delayed observations and unknown variance

Sequential stochastic optimization has been used in many contexts, from simulation, to e-commerce, to clinical trials. Much of this analysis assumes that observations are made soon after a sampling decision is made, so that the next sampling decision can benefit from the most recent data. This assumption is not true in a number of contexts, including clinical trials. In this paper we extend sequential sampling tools from simulation optimization to be useful when there exists a delay in observing the data from sampling, with a specific focus on the situation in which the sampling variance is unknown. We demonstrate the benefits of doing so by benchmarking the optimization algorithms with data from a published clinical trial.