| We consider the Bayesian formulation of a number of learning problems, where we focus on sequential sampling procedures for allocating simulation effort efficiently.;We derive Bayes-optimal policies for the problem of multiple comparisons with a known standard, showing that they can be computed efficiently when sampling is limited by probabilistic termination or sampling costs. We provide a tractable method for computing upper bounds on the Bayes-optimal value of a ranking and selection problem, which enables evaluation of optimality gaps for existing ranking and selection procedures. Applying techniques from optimal stopping, multi-armed bandits and Lagrangian relaxation, we are able to efficiently solve the corresponding dynamic programs.;We develop a new value-of-information-based procedure for the problem of Bayesian optimization via simulation, which incorporates both correlated prior beliefs and correlated sampling distributions. We also introduce a sequential Bayesian algorithm for optimization of expensive functions under low-dimensional input uncertainties. These implementations take advantage of machine learning tools that enable exploring combinatorially large solution spaces, or estimating expectations of simulation output variables with random inputs.;We present theoretical results characterizing the proposed procedures, compare them numerically against previously developed or standard benchmarking procedures, and apply them to applications in emergency services, manufacturing, and health care. |
