  In a fixed budget ranking and Selection (R&S) problem, one aims to identify
the best design among a finite number of candidates by efficiently allocating
the given computing budget to evaluate design performance. Classical methods
for R&S usually assume the distribution of the randomness in the system is
exactly known. In this paper, we consider the practical scenario where the true
distribution is unknown but can be estimated from streaming input data that
arrive in batches over time. We formulate the R&S problem in this dynamic
setting as a multi-stage problem, where we adopt the Bayesian approach to
estimate the distribution and formulate a stage-wise optimization problem to
allocate the computing budget. We characterize the optimality conditions for
the stage-wise problem by applying the large deviations theory to maximize the
decay rate of probability of false selection. Based on the optimality
conditions and combined with the updating of distribution estimates, we design
two sequential budget allocation procedures for R&S under streaming input data.
We theoretically guarantee the consistency and asymptotic optimality of the
proposed procedures. We demonstrate the practical efficiency through numerical
experiments in comparison with the equal allocation policy and an extension of
the Optimal Computing Budget Allocation algorithm.
