Posterior Distribution-assisted Evolutionary Dynamic Optimization as an Online Calibrator for Complex Social Simulations

TL;DR

This work reframes online calibration of complex social-system simulators as a dynamic optimization problem driven by streaming observations. It introduces PosEDO, a posterior-distribution–guided framework that learns a flow-based posterior $p_{\phi}(\bm{\theta}|\{\hat{\bm{s}}_t\})$, enabling robust change detection via $D_{KL}$ and efficient environment adaptation through posterior-guided sampling. Empirical results on Brock-Hommes and PGPS simulators show PosEDO outperforms traditional EDO baselines in both calibration accuracy and convergence stability, with ablations confirming the value of online posterior refinement. The approach offers a principled way to handle data-driven environmental changes in online optimization and has potential for broader applications in online learning and symbolic regression.

Abstract

The calibration of simulators for complex social systems aims to identify the optimal parameter that drives the output of the simulator best matching the target data observed from the system. As many social systems may change internally over time, calibration naturally becomes an online task, requiring parameters to be updated continuously to maintain the simulator's fidelity. In this work, the online setting is first formulated as a dynamic optimization problem (DOP), requiring the search for a sequence of optimal parameters that fit the simulator to real system changes. However, in contrast to traditional DOP formulations, online calibration explicitly incorporates the observational data as the driver of environmental dynamics. Due to this fundamental difference, existing Evolutionary Dynamic Optimization (EDO) methods, despite being extensively studied for black-box DOPs, are ill-equipped to handle such a scenario. As a result, online calibration problems constitute a new set of challenging DOPs. Here, we propose to explicitly learn the posterior distributions of the parameters and the observational data, thereby facilitating both change detection and environmental adaptation of existing EDOs for this scenario. We thus present a pretrained posterior model for implementation, and fine-tune it during the optimization. Extensive tests on both economic and financial simulators verify that the posterior distribution strongly promotes EDOs in such DOPs widely existed in social science.

Figures (4)

• Figure 1: Comparison of detection accuracy across 9 benchmark instances ($F_1$--$F_9$) on the Brock--Hommes model. In each subplot, the red dashed lines indicate the ground-truth change points. The purple, blue, and orange curves represent the change detection probability densities of FBCD-Rand, DBD-Rand, and PosEDO-CD, respectively.
• Figure 2: Change detection accuracy under different thresholds $\varepsilon$ on instance $F_8$ of the Brock–Hommes model. The subplot (a) summarizes low-threshold cases ($\varepsilon=5,15,30$); and subplot (b) shows higher thresholds ($\varepsilon=100,120$). Red dashed lines mark the ground-truth change points for comparison.
• Figure 3: Under the assumption that the change points are correctly detected, the calibration error comparison of NNIT, Arch, Rand, and PosEDO-Ada across 9 instances ($F_1$--$F_9$) on the Brock–Hommes model. The horizontal axis represents the iterations, and the vertical axis represents the error value in log scale. And the vertical dashed lines indicate the true changes.
• Figure 4: Detection accuracy comparison across 9 problem instances ($F_1$–$F_9$) on the PGPS model. In each subplot, the red dashed lines indicate the ground-truth change times. The purple, blue, and orange curves represent the change detection probability densities of FBCD-Rand, DBD-Rand, and PosEDO-CD, respectively.