Online Inverse Optimal Transport for Societal Flows
Lead Research Organisation:
Imperial College London
Department Name: Mathematics
Abstract
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.
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.
Organisations
Publications
Athanasiades, R.
(2023)
Redefining Pedestrian Motion: A Novel, Data-Driven Approach via Inverse Reinforcement Learning
Düring B
(2024)
Breaking Consensus in Kinetic Opinion Formation Models on Graphons
in Journal of Nonlinear Science
Düring B
(2024)
Breaking Consensus in Kinetic Opinion Formation Models on Graphons
Gaskin T
(2024)
Modelling Global Trade with Optimal Transport
Nugent A
(2024)
Steering opinion dynamics through control of social networks
in Chaos: An Interdisciplinary Journal of Nonlinear Science
Nugent A
(2024)
Steering opinion dynamics through control of social networks
| Description | This work has opened the door to a new class of methods for dealing with complex flow based data, where the quantification of uncertainty matters. The original emphasis of the grant was on the challenge of Inverse Optimal Transport, i.e. recovering the cost function driving a flow of decision makers. However, since then it has become clear that there are far more fundamental inference challenges around flows. Based on this, we have developed two new methods (publications still in progress, but preprints to appear soon), which can be leveraged -- one of them leveraging deep neural networks to provide a highly expressive model of flow-based systems, and another non-parameteric model providing a fully Bayesian approach to this problem. The original goal of the project was to use FAOStat data (food commodity flows) and UNHRC migration flow data as case-studies. Since then we have worked with researchers and stakeholders who actively work in these fields (Guy Abel, U of Hong Kong) and (Guven Dumeriel, QMUL), who have provided us with crucial context and validation on the utility of these new methods. The research question has expanded dramatically, and this work will remain ongoing -- initial unfunded, and then followed-up through further grant funding. |
| Exploitation Route | One of the opportunities we have identified from this research is the need for the development of a software framework to do inference for noisy flows. Although this was not within the original award proposal, we now realise the priority of this. We are currently seeking to develop this, seeking funding from external organisations (e.g. GSOC etc) to be able to develop this. We have also had very strong interest by partners working in Defence and National Security around the potential use of this technology to drive analysis and decision support around migratory flows and crisis relief. We are currently working with an SME to make this a possibility and secure further funding. |
| Sectors | Security and Diplomacy |