Fixed Budget Ranking and Selection with Streaming Input Data

We consider a fixed budget ranking and selection problem with input uncertainty, where unknown input distributions can be estimated using input data arriving in batches of varying sizes over time. Each time a batch arrives, the input distribution is updated and additional simulations can be run with a given simulation budget. Within each time stage, we apply the large deviations theory to compute the rate function of the probability of false selection (PFS) with input distribution and formulate an optimization problem to maximize the decay rate of PFS. With the derived optimality condition, we design a dynamic optimal budget allocation procedure with sequentially updated input distributions under streaming input data. We prove the consistency and asymptotic optimality of the procedure, and numerically show the high efficiency of our procedure compared to the equal allocation rule and a simple extension of the Optimal Computing Budget Allocation (OCBA) algorithm.