Koopman-Based Surrogate Models for Multi-Objective Optimization of Agent-Based Systems

TL;DR

This paper introduces a data-driven Koopman generator-based surrogate modeling approach to efficiently solve multi-objective optimization problems in complex, high-dimensional agent-based systems like voter and epidemic models.

Contribution

It develops a novel Koopman-based reduced model framework for non-deterministic ABMs, enabling efficient multi-objective optimization and decision-making support.

Findings

Surrogate models accurately approximate Pareto-optimal solutions.

The approach reduces computational costs for high-dimensional ABMs.

Effective in controlling voter and epidemic agent-based systems.

Abstract

Agent-based models (ABMs) provide an intuitive and powerful framework for studying social dynamics by modeling the interactions of individuals from the perspective of each individual. In addition to simulating and forecasting the dynamics of ABMs, the demand to solve optimization problems to support, for example, decision-making processes naturally arises. Most ABMs, however, are non-deterministic, high-dimensional dynamical systems, so objectives defined in terms of their behavior are computationally expensive. In particular, if the number of agents is large, evaluating the objective functions often becomes prohibitively time-consuming. We consider data-driven reduced models based on the Koopman generator to enable the efficient solution of multi-objective optimization problems involving ABMs. In a first step, we show how to obtain data-driven reduced models of non-deterministic dynamical systems (such as ABMs) that depend potentially nonlinearly on control inputs. We then use them in the second step as surrogate models to solve multi-objective optimal control problems. We first illustrate our approach using the example of a voter model, where we compute optimal controls to steer the agents to a predetermined majority, and then using the example of an epidemic ABM, where we compute optimal containment strategies in a prototypical situation. We demonstrate that the surrogate models effectively approximate the Pareto-optimal points of the ABM dynamics by comparing the surrogate-based results with test points, where the objectives are evaluated using the ABM. Our results show that when objectives are defined by the dynamic behavior of ABMs, data-driven surrogate models support or even enable the solution of multi-objective optimization problems.