Online Inverse Optimal Transport for Societal Flows

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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.