Stochastic Approximation for simulation Optimization under Input Uncertainty with Streaming Data

Abstract

We consider a simulation optimization problem whose objective function is defined as the expectation of a simulation output based on a continuous decision variable, where the parameters of the simulation input distributions are estimated based on independent and identically distributed streaming data from a real-world system. Finite-sample error in the input parameter estimates causes input uncertainty in the simulation output, which decreases as the data size increases. By viewing the problem through the lens of misspecified stochastic optimization, we develop a stochastic approximation (SA) framework to solve a sequence of problems defined by the sequence of input parameter estimates to increasing levels of exactness. Under suitable assumptions, we observe that the error in the SA solution diminishes to zero in expectation and propose a SA sampling scheme so that the resulting solution iterates converge to the optimal solution under the real-world input distribution at the best possible rate.