A Bayesian Approach to Online Simulation Optimization with Streaming Input Data

We consider simulation optimization under input uncertainty, where the unknown input parameter is estimated from streaming data arriving in batches over time. Moreover, data may depend on the decision of the time when they are generated. We take an online approach to jointly estimate the input parameter via Bayesian posterior distribution and update the decision by applying stochastic gradient descent (SGD) on the Bayesian average of the objective function. We show the convergence of our approach. In particular, our consistency result of Bayesian posterior distribution with decision-dependent data might be of independent interest to Bayesian estimation. We demonstrate the empirical performance of our approach on a simple numerical example.