论文标题
大流行的最佳政策：随机游戏方法和深度学习算法
Optimal Policies for a Pandemic: A Stochastic Game Approach and a Deep Learning Algorithm
论文作者
论文摘要
游戏理论一直是控制疾病传播以及提出个人和地区层面最佳政策的有效工具。在本文中，我们提出了一个基于随机差异游戏理论的多区域SEIR模型，旨在制定传染病的最佳区域政策。具体而言，我们通过考虑多个地区规划师发布的社会和健康政策来增强标准流行病模型。这种增强使模型更现实和强大。但是，由于多个区域的存在带来的解决方案空间的高维度，它也引入了巨大的计算挑战。模型结构的这一重大数值难度激发了我们推广[Han and Hu，MSML2020，pp.221--245，PMLR，2020]中引入的深层虚拟算法，并开发了改进的算法以克服维度的诅咒。我们将提出的模型和算法应用于三个州的COVID-19大流行：纽约，新泽西州和宾夕法尼亚州。该模型参数是根据疾病控制与预防中心（CDC）发布的实际数据估算的。我们能够展示锁定/旅行禁令政策对每个州Covid-19的传播以及其政策如何相互影响的影响。
Game theory has been an effective tool in the control of disease spread and in suggesting optimal policies at both individual and area levels. In this paper, we propose a multi-region SEIR model based on stochastic differential game theory, aiming to formulate optimal regional policies for infectious diseases. Specifically, we enhance the standard epidemic SEIR model by taking into account the social and health policies issued by multiple region planners. This enhancement makes the model more realistic and powerful. However, it also introduces a formidable computational challenge due to the high dimensionality of the solution space brought by the presence of multiple regions. This significant numerical difficulty of the model structure motivates us to generalize the deep fictitious algorithm introduced in [Han and Hu, MSML2020, pp.221--245, PMLR, 2020] and develop an improved algorithm to overcome the curse of dimensionality. We apply the proposed model and algorithm to study the COVID-19 pandemic in three states: New York, New Jersey, and Pennsylvania. The model parameters are estimated from real data posted by the Centers for Disease Control and Prevention (CDC). We are able to show the effects of the lockdown/travel ban policy on the spread of COVID-19 for each state and how their policies affect each other.
