Automatic Gradient Estimation for Calibrating Crowd Models with Discrete Decision Making

TL;DR

The paper tackles calibrating crowd evacuation simulations with discrete decision making using gradient-based optimization. It develops the DiscoGrad Gradient Oracle, derives it from stratified derivatives, and compares AD-based and stochastic gradient estimators against gradient-free methods across two evacuation scenarios. Key contributions include an alternative DiscoGrad derivation, analysis of gradient fidelity on rugged evacuation surfaces, and showing that calibrating a per-agent decision-distribution in a $20$-dimensional space can be efficiently optimized with gradient descent while reducing automatic-differentiation overhead. The findings highlight when gradient-based methods are advantageous and suggest model refinements to reduce abrupt jumps without sacrificing realism, enabling more efficient calibration of complex agent-based simulations.

Abstract

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.

Figures (9)

• Figure 1: Scenario for calibrating exit selection coefficients. The crowd enters from the left-hand side, aiming to evacuate by reaching the circular waypoints (dashed circles), each agent periodically reconsidering the targeted exit by weighing its distance against the number of agents in its vicinity (gray circles).
• Figure 2: Derivative estimates with respect to the weight of the three types of forces in scenarios populated with 3 agents (a-c) and 10 agents (d-f) with the fit in the agents' final coordinates' as output and $\sigma = 0.001$. PGO with a large number of samples is used as the reference. DGO captures most of the derivatives' spikes, whereas the IPA estimate only reflects the general curvature.
• Figure 3: Derivative estimates with respect to the weight of the internal force, the simulation output being the fit in the number of evacuations. In the larger scenario, DGO's estimates suffer from substantial noise as jumps in the mobility derivatives translate to biased and high-variance derivative estimates of the simulation output. When ignoring jumps in the Social Force model (IPA/DGO), estimates observe some bias but capture the trends well.
• Figure 4: MAE of gradients wrt. $w_0$ fitting the agent coordinates, $\sigma = 0.001$.
• Figure 5: MAE of gradients wrt. $w_0$ fitting the evacuation count, $\sigma = 0.001$.