Slight Stochastic Shifts Suffice: Cross-Trajectory Vectorized Estimation of Simulation Gradients

Monte Carlo gradient estimators enable an efficient gradient-driven local search in a simulation’s parameter space. Partial derivatives are estimated based on the simulation outputs at random perturbations around the current parameter combination. However, the effective computational cost grows with the number of perturbations. Here, we explore the use of modern CPUs’ vector instructions to reduce the estimation time on a single processor core. We vectorize across simulation trajectories, based on the hypothesis that the perturbations can be chosen small enough that the control flow divergence remains low. Control flow is realized using a predication scheme, allowing model code to remain similar to its scalar counterpart. Since the approach trivially benefits numerical simulations without parameter-dependent control flow, our evaluation instead considers the calibration of a building evacuation model in which transitive effects of perturbations change the neighborhood relation among pedestrians. Our cross-trajectory vectorization scheme speeds up the model’s calibration via simulation-based inference by a factor of about 1.5 without occupying additional cores.