Nash Neural Networks: Inferring Utilities from Optimal Behaviour in Epidemics

这个博士项目是关于将控制理论应用于流行病学问题。在这项工作中，我们将把个人视为理性的代理人，他们在面对传染病时寻求最大限度地提高自己的福祉。我们将采用一种新的方法来学习目标为纳什均衡的个人的隐藏偏好，使用类似于物理学通知机器学习（例如拉格朗日神经网络）的最新发展的机器学习方法。该项目的主要目标包括寻求整合拉格朗日乘数，以便仅从可观测信息（即流行病的SIR动态）中学习效用，并考虑直接/逆最优控制问题的不同形式的效用。然而，这项研究还有其他的和潜在的进一步目标。例如，从开放源代码、人口水平的数据推断实用程序。由此，我们可以探索纳什代理的最优政府控制和推断政府目标，并与他们提出的目标进行比较。还可以探索我们的流行病模型的扩展，例如将不确定性（随机最优控制）普遍化，并利用数据中的不同区域（例如年轻人和老年人）。研究方法的新颖性：您推断符合纳什均衡的效用的方法是完全新颖的。与之前的方法相反，我们不需要假设个人偏好的功能形式。这种新颖性的进一步方面包括在流行病中饱和的卫生保健系统的作用，以及项目后期个人可获得的信息中的不确定性的作用。潜在的影响、应用和益处我们认为，迫切需要定量的政策制定工具来帮助管理未来的传染病流行。这可能也适用于其他社会规划问题。这项工作的可能扩展包括修改目标函数（效用），以模仿文献中使用的其他形式或更准确的模型。在项目的后期，我们寻找相关领域的应用，包括经济、金融或群体行为。从根本上说，我们的工作涉及开发一种新的机器学习方法，应用于控制理论，这是一个工程领域。研究分为工程、全球不确定性和医疗保健技术研究领域。外部合作伙伴-京都大学软物质工程实验室-山本良一教授（京都大学化学工程系软物质工程）。与约翰·莫利纳博士和西蒙·施奈德博士一起，他们开发了新的计算技术来模拟复杂的软物质系统，包括胶体分散、细胞组织和聚合物熔体流动等。最近，他们与Matthew Turner教授（博士生导师）合作，致力于为理性个体社会中的定量政策制定建立理论框架。特别是，他们研究了如何利用税收和/或政府补贴，使大流行期间做出理性决策的个人与社会最优行为保持一致，比如正在进行的SARS-CoV-2全球大流行。外部合作伙伴已同意为该项目的机器学习应用提供所需的高性能计算资源（东京大学，wisteria - bdec 01， NVIDIA A100 GPU集群）的技术支持和访问。合作伙伴已同意参加两周一次的（远程）会议，讨论工作的建模和技术方面。此外，合作伙伴已经同意在京都接待我进行部分博士研究。

The context of the researchThis PhD project is concerned with applying control-theory to epidemiological problems. In this work we will treat individuals as rational agents who seek to maximise their well-being in the face of an infectious disease. The aims and objectives of the researchWe will employ a new methodology for learning hidden preferences for individuals who target a Nash Equilibrium using Machine learning approach similar to recent develops in Physics Informed Machine Learning (e.g Lagrangian Neural Networks).The main objectives of this project include seeking to integrate out the Lagrange multipliers in order to learn the utility soley from observable information (i.e the SIR dynamics of the epidemic) and to consider different forms of the utility for both direct/inverse optimal control problems. There are, however, alternative and potential furhter aims of the research. Such as inferring utilities from open source, opulation-level data. From this we could explore optimal governemtn control of Nash agents and inferring government objectivesm with which to compare against their proposed objectives. Extensions to our epidemics model can also be explored, such as gerneralising to include uncertainty (stochastic optimal control) and utilising different compartments in our data (e.g young and old individuals).The novelty of the research methodologyOur approach for inferring utilities consistent with a Nash equilibrium is completlty novel. In contrast to previous approached we do not need to assume the functional form of the individual preferences. Further aspect of the novelty include the role of saturating health-care systems in pandemics, later in the project the role of uncertainties in the infomraiton available to individuals.The potential impact, applications and benefitsWe believe there is a pressing need for qunatitative policy making tools to help manage future epidemics of infectious diseases. This may also have applications in other social planning problems.Possible extensions to this work include modification of the objective function (utility) to mimic other forms used in the literature or more accurate models. Later in the project we look for applications in related fields, including economics, finance or swarm behaviour.How the research relates to the remitFundamentally our work involves developing a new ML approach, applied to control theory, a field in engineering. The research falls into the Engineering, Global uncertainties and Healthcare technologies research areas.External partner - soft Matter Engineering Lab, Kyoto University - Prof. Ryoichi Yamamoto (Soft Matter Engineering, Department of Chemical Enginerering, Kyoto University). Together with Drs John Molina and Simon Schnyderr they have devleoped novel computational techniques for simulating complex Soft Matter Systems, including colloidal dispersions, celluar tissues, and ploymer melt flows, among others. More recently, in collaboration with Prof. Matthew Turner (PhD supervisor 1), they have worked to establish a theorectical framework for qunatitative poliymaking in a society of rational individuals. In particular, they have studied how taxes and/or government subsidies can be used to align the decison making rational individuals with the socially optimal behaviour during the pandemic, like the ongoing SARS-CoV-2 global pandeimic.The external partner has agreed to provide technical support and access to high-performance computing resources (Tokyo Univerisyt, Wisterria-BDEC 01, NVIDIA A100 GPU cluster) required for the Machine learning applications of this prokect. The partner has agreed to attend bi-weekly (remote) meetings to discuss the modelling and technical aspects of the work. In addition, the partner has agreed to host me in Kyoto for part of my PhD studies.