Biased Gradient Estimators in Simulation Optimization

Within the simulation community, the prevailing wisdom seems to be that when solving a simulation optimization problem, biased gradient estimators should not be used to guide a local-search algorithm. On the contrary, we argue that for certain problems, biased gradient estimators may still provide useful directional information. We focus on the infinitesimal perturbation analysis (IPA) gradient estimator, which is biased when an interchange of differentiation and expectation fails. Although a local-search algorithm guided by biased gradient estimators will likely not converge to a local optimal solution, it might be expected to reach a neighborhood of one. We test such a gradient-based search on an ambulance base location problem, demonstrating its effectiveness in a non-trivial example, and present some supporting theoretical results.