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

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.

Calibrating Agent-Based Financial Markets Simulators with Pretrainable Automatic Posterior Transformation-Based Surrogates

Calibrating Agent-Based Models (ABMs) is an important optimization problem for simulating the complex social systems, where the goal is to identify the optimal parameter of a given ABM by minimizing the discrepancy between the simulated data and the real-world observations. Unfortunately, it suffers from the extensive computational costs of iterative evaluations, which involves the expensive simulation with the candidate parameter. While Surrogate-Assisted Evolutionary Algorithms (SAEAs) have been widely adopted to alleviate the computational burden, existing methods face two key limitations: 1) surrogating the original evaluation function is hard due the nonlinear yet multi-modal nature of the ABMs, and 2) the commonly used surrogates cannot share the optimization experience among multiple calibration tasks, making the batched calibration less effective. To address these issues, this work proposes Automatic posterior transformation with Negatively Correlated Search and Adaptive Trust-Region (ANTR). ANTR first replaces the traditional surrogates with a pretrainable neural density estimator that directly models the posterior distribution of the parameters given observed data, thereby aligning the optimization objective with parameter-space accuracy. Furthermore, we incorporate a diversity-preserving search strategy to prevent premature convergence and an adaptive trust-region method to efficiently allocate computational resources. We take two representative ABM-based financial market simulators as the test bench as due to the high non-linearity. Experiments demonstrate that the proposed ANTR significantly outperforms conventional metaheuristics and state-of-the-art SAEAs in both calibration accuracy and computational efficiency, particularly in batch calibration scenarios across multiple market conditions.