Optimal control of agent-based models via surrogate modeling

This paper describes and validates an algorithm to solve optimal control problems for agent-based models (ABMs). For a given ABM and a given optimal control problem, the algorithm derives a surrogate model, typically lower-dimensional, in the form of a system of ordinary differential equations (ODEs), solves the control problem for the surrogate model, and then transfers the solution back to the original ABM. It applies to quite general ABMs and offers several options for the ODE structure, depending on what information about the ABM is to be used. There is a broad range of applications for such an algorithm, since ABMs are used widely in the life sciences, such as ecology, epidemiology, and biomedicine and healthcare, areas where optimal control is an important purpose for modeling, such as for medical digital twin technology.Author summary: The motivation for the work reported in this paper is the development of mathematical tools for medical digital twins. Based on a computational model of some aspects of human biology, there is a two-way interaction between the physical twin (the patient) and the digital twin (the model). In one direction, the model is periodically calibrated with patient-derived data to evolve alongside the patient, transforming it into a digital twin. In the other direction, optimal interventions derived from the digital twin are administered to the patient. In many cases, there is a lack of readily available methods for optimal control in the underlying computational model, making it challenging to identify effective interventions. This is particularly true for model types such as agent-based models (ABMs), which are often more suitable in the context of medical digital twins than models based on ordinary differential equations (ODEs). In this paper, we present an algorithm that takes a general ABM and an optimal control problem as inputs and provides a solution to the control problem as output. This is accomplished by first constructing a surrogate ODE model, solving the optimal control problem, and then transferring the solution back to the ABM. The algorithm supports several types of surrogate models, ranging from those that implement mechanistic features of the ABM to purely phenomenological models. The algorithm is validated by applying it to a predator-prey ABM and a metabolic network represented as an ABM.