Hierarchical clustering and dimensional reduction for optimal control of large-scale agent-based models

Abstract: Agent-based models (ABMs) provide a powerful framework to describe complex systems composed of interacting entities, capable of producing emergent collective behaviours such as consensus formation or clustering. However, the increasing dimensionality of these models- in terms of both the number of agents and the size of their state space- poses significant computational challenges, particularly in the context of optimal control. In this work, we propose a scalable control frame work for large-scale ABMs based on a twofold model order reduction strategy: agent clustering and projection-based reduction via Proper Orthogonal Decomposition (POD). These techniques are integrated into a feedback loop that enables the design and application of optimal control laws over a reduced-order representation of the system. To illustrate the effectiveness of the approach, we consider the opinion dynamics model, a prototyp ical first-order ABM where agents interact through state-dependent influence functions. We show that our method significantly improves control efficiency, even in scenarios where direct control fails due to model complexity. Beyond its methodological contributions, this work also highlights the rel evance of opinion dynamics models in environmental contexts- for example, modeling the diffusion of pro-environmental attitudes or decision-making processes in sustainable policy adoption- where controlling consensus formation plays a crucial role.