Data-driven Control of Agent-based Models: an Equation/Variable-free Machine Learning Approach

TL;DR

This paper introduces an equation/variable-free machine learning framework for controlling complex agent-based systems by identifying low-dimensional manifolds, performing bifurcation analysis, and designing robust data-driven controllers without explicit model construction.

Contribution

It presents a novel, model-free approach combining manifold learning, bifurcation analysis, and control design for agent-based models, avoiding the need for surrogate models.

Findings

Successfully controlled unstable traveling waves in traffic models

Achieved stabilization of equilibria in stochastic financial market models

Demonstrated robustness against modeling uncertainties

Abstract

We present an Equation/Variable free machine learning (EVFML) framework for the control of the collective dynamics of complex/multiscale systems modelled via microscopic/agent-based simulators. The approach obviates the need for construction of surrogate, reduced-order models.~The proposed implementation consists of three steps: (A) from high-dimensional agent-based simulations, machine learning (in particular, non-linear manifold learning (Diffusion Maps (DMs)) helps identify a set of coarse-grained variables that parametrize the low-dimensional manifold on which the emergent/collective dynamics evolve. The out-of-sample extension and pre-image problems, i.e. the construction of non-linear mappings from the high-dimensional input space to the low-dimensional manifold and back, are solved by coupling DMs with the Nystrom extension and Geometric Harmonics, respectively; (B) having identified the manifold and its coordinates, we exploit the Equation-free approach to perform numerical bifurcation analysis of the emergent dynamics; then (C) based on the previous steps, we design data-driven embedded wash-out controllers that drive the agent-based simulators to their intrinsic, imprecisely known, emergent open-loop unstable steady-states, thus demonstrating that the scheme is robust against numerical approximation errors and modelling uncertainty.~The efficiency of the framework is illustrated by controlling emergent unstable (i) traveling waves of a deterministic agent-based model of traffic dynamics, and (ii) equilibria of a stochastic financial market agent model with mimesis.