Approximate Bayesian inference for simulation and optimization

We present an overview of approximate Bayesian methods for sequential learning in problems where conjugate Bayesian priors are unsuitable or unavailable. Such problems have numerous applications in simulation optimization, revenue management, e-commerce, and the design of competitive events. We discuss two important computational strategies for learning in such applications, and illustrate each strategy with multiple examples from the recent literature. We also briefly describe conjugate Bayesian models for comparison, and remark on the theoretical challenges of approximate models.