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.

翻译：种群动力学的研究起源于早期社会学著作，但现已扩展到许多领域，包括生物学、流行病学、演化博弈论和经济学。大多数关于种群动力学的研究侧重于预测而非控制问题。现有的种群动力学控制数学模型通常局限于特定的无噪声动态，而现实世界的种群变化可能复杂且具有对抗性。为弥补这一不足，我们基于在线控制范式提出了一种新框架。我们首先刻画了一组能够自然建模演化种群的线性动态系统。随后，我们为这些系统提出了一种高效的基于梯度的控制器，其相对于广泛线性策略类具有近乎最优的遗憾界。实证评估表明，所提算法在种群动力学控制中具有有效性，即使对于SIR模型和复制动力学等非线性模型亦是如此。