Nash Neural Networks: Inferring Utilities from Optimal Behaviour in Epidemics

研究背景这个博士项目涉及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。研究的目的和目标我们将采用一种新的方法来学习个人的隐藏偏好，这些人使用机器学习方法来实现纳什均衡，类似于最近在物理信息机器学习中的发展该项目的主要目标包括寻求整合出拉格朗日乘子，以便从可观察的信息中学习效用（即SIR动态的流行病），并考虑不同形式的直接/逆最优控制问题的效用。然而，研究还有其他的和潜在的更进一步的目的。比如从开源的、高水平的数据中推断出公用事业。由此，我们可以探索纳什代理人的最佳governemtn控制，并推断政府目标，与他们提出的目标进行比较。我们的流行病模型的扩展也可以探索，如gerneralising包括不确定性（随机最优控制）和利用不同的隔间在我们的数据（例如年轻人和老年人）。新奇的研究方法我们的方法推断效用符合纳什均衡是completlty新颖。与前面的方法相反，我们不需要假设个人偏好的函数形式。新奇的进一步方面包括饱和的卫生保健系统在流行病中的作用，稍后在该项目中的不确定性在个人可获得的信息中的作用。潜在的影响，应用和效益我们认为，迫切需要定量的政策制定工具，以帮助管理未来的传染病流行。这也可能在其他社会规划问题中有应用。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精确的模型。在项目的后期，我们将寻找相关领域的应用，包括经济学、金融学或群体行为。研究如何与根本上我们的工作涉及开发一种新的ML方法，应用于控制理论，这是一个工程领域。研究福尔斯属于工程学、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）。他们与John Molina和Simon Schnyderr博士一起开发了用于模拟复杂软物质系统的新型计算技术，包括胶体分散体，细胞组织和聚合物熔体流动等。最近，与Matthew Turner教授（博士生导师1）合作，他们致力于建立一个理论框架，用于在理性个体的社会中进行定量决策。特别是，他们研究了如何利用税收和/或政府补贴，使决策理性的个人与流行病期间的社会最佳行为保持一致，例如正在进行的SARS-CoV-2全球流行病。外部合作伙伴已同意提供技术支持和高性能计算资源的使用权（Tokyo Univerisyt，Wisteria-BDEC 01，NVIDIA A100 GPU集群）。合作伙伴同意参加每两周一次的（远程）会议，讨论工作的建模和技术方面。此外，合作伙伴已同意接待我在京都为我的博士研究的一部分。

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.