Automatic Gradient Estimation for Calibrating Crowd Models with Discrete
  Decision Making
Philipp Andelfinger Justin N. Kreikemeyer
Recently proposed gradient estimators enable gradient descent over stochastic
programs with discrete jumps in the response surface, which are not covered by
automatic differentiation (AD) alone. Although these estimators' capability to
guide a swift local search has been shown for certain problems, their
applicability to models relevant to real-world applications remains largely
unexplored. As the gradients governing the choice in candidate solutions are
calculated from sampled simulation trajectories, the optimization procedure
bears similarities to metaheuristics such as particle swarm optimization, which
puts the focus on the different methods' calibration progress per function
evaluation. Here, we consider the calibration of force-based crowd evacuation
models based on the popular Social Force model augmented by discrete decision
making. After studying the ability of an AD-based estimator for branching
programs to capture the simulation's rugged response surface, calibration
problems are tackled using gradient descent and two metaheuristics. As our main
insights, we find 1) that the estimation's fidelity benefits from disregarding
jumps of large magnitude inherent to the Social Force model, and 2) that the
common problem of calibration by adjusting a simulation input distribution
obviates the need for AD across the Social Force calculations, allowing
gradient descent to excel.