A Variance-Adaptive Lower Bound for Simulation Optimization in Continuous Space

This paper considers the simulation optimization with continuous decision variables. Under certain reasonable assumptions, we provide a worst-case lower bound on the optimization error for any algorithms. The lower bound can incorporate the noiseless and noisy problems in an unified framework. The result highlights that the optimization error of noisy problems can be very close to that of noiseless problems when the observation's variance is small and the budget is not very large.