Online Control in Population Dynamics

TL;DR

This paper introduces an online control framework for population dynamics, enabling effective management of complex and adversarial population changes with near-optimal regret bounds, applicable to both linear and non-linear models.

Contribution

It proposes a new online control approach for population dynamics, including a gradient-based controller with theoretical regret guarantees and empirical validation on various models.

Findings

Effective control achieved in linear population models.

Demonstrated applicability to non-linear models like SIR and replicator dynamics.

Near-optimal regret bounds established for the proposed control method.

Abstract

The study of population dynamics originated with early sociological works but has since extended into many fields, including biology, epidemiology, evolutionary game theory, and economics. Most studies on population dynamics focus on the problem of prediction rather than control. Existing mathematical models for control in population dynamics are often restricted to specific, noise-free dynamics, while real-world population changes can be complex and adversarial. To address this gap, we propose a new framework based on the paradigm of online control. We first characterize a set of linear dynamical systems that can naturally model evolving populations. We then give an efficient gradient-based controller for these systems, with near-optimal regret bounds with respect to a broad class of linear policies. Our empirical evaluations demonstrate the effectiveness of the proposed algorithm for control in population dynamics even for non-linear models such as SIR and replicator dynamics.