Online Inverse Optimal Transport for Societal Flows

社会科学和自然科学中有许多过程，可以被视为人员、商品或财富从一组地点/国家流向另一组地点/国家。在许多这样的情况下，这些流动是由一些潜在的成本标准决定的最佳情况。例如，通过这种视角观察移民或难民从一个国家到另一个国家的流动，使我们能够了解相关个人的动机，这有助于确定长期趋势并支持政策制定。我们对这样一种情况感兴趣，即我们对这种流动进行了测量，并希望推断推动这种流动的潜在成本/激励标准。这个问题被称为逆最优运输(IOT)，它是许多重要应用的核心，从经济学、人口统计学研究和城市规划到交通和物流。它也有许多与机器学习中研究的类似问题的共同特征，如逆强化学习和地面度量学习。在这项工作中，我们试图通过两个重要的方式来扩展物联网框架的适用性。首先，我们将开发新的物联网方法，这些方法对不完整、不一致和有噪声的数据具有健壮性。在研究任何真实世界的流动(如迁徙或商品流动)时，拥有不可靠的数据是常态，因此能够吸收此类数据是在此类情景中利用物联网方法的先决条件。其次，我们的目标是开发新的方法来解决流数据情况下的物联网问题，在这种情况下，流的特征是大量的分类数据，随着时间的推移而演变。要以有效的方式处理如此丰富的数据，需要采用新的方法来解决这个问题。扩展物联网方法的适用性是开发可靠的、不断更新的此类过程模型的第一步。这将为社会流动的数字孪生兄弟铺平道路，旨在支持对这些复杂现象的监测、预测和决策。

There are many processes in social sciences and natural sciences which can be viewed as flows of people, commodities or wealth from one set of locations / states to another. In many such cases, these flows occur optimally, determined by some underlying cost criterion. For example, viewing flows of migrants or refugees from one country to another through this lens permits us to understand the incentives of the individuals involved, which can help identify long-term trends and support policy-making.We are interested in the situation where we have measurements of such a flow and wish to infer the underlying cost/incentive criterion which is driving it. This problem, known as Inverse Optimal Transport (IOT), lies at the core of many important applications, ranging from economics, demographic research and urban planning to transportation and logistics. It also shares many common features with similar problems studied in Machine Learning such as Inverse Reinforcement Learning and Ground Metric Learning.In this work we seek to extend the applicability of the IOT framework in two important ways. Firstly, we will develop new approaches to IOT which are robust to incomplete, inconsistent and noisy data. Having unreliable data is the norm when studying any real-world flows such a migratory or commodity flows, and so being able to assimilate such data is a prerequisite to leveraging IOT methodology in such scenarios. Secondly, we aim to develop new methods to solve IOT problems in streaming data situations, where flows are characterised by large volumes of disaggregated data, evolving over time. To handle this abundance of data in an efficient manner requires new approaches to this problem. Extending the applicability of the IOT methodology is a first step in developing reliable, continuously-updating models of such processes. This would pave the way for digital twins of societal flows, built to support monitoring, forecasting and decision-making for these complex phenomena.