Optimal Transport–Based Nonlinear Filtering
Overview
Quantifying uncertainty and effectively assimilating noisy sensory data is the subject of nonlinear filtering, and is crucial for the reliable and safe operation of robotic systems. Classical nonlinear filtering algorithms, such as Kalman filter and its extensions, or sequential importance sampling particle filters, are subject to fundamental limitations and do not perform well in the nonlinear and high-dimensional settings. This research aims to overcome these challenges by merging the recent developments in machine learning (ML) and optimal transportation (OT) to construct nonlinear filtering algorithms with increased flexibility, scalability, and adaptability. This is achieved through the utilization of a novel variational formulation of Bayes’ law, rooted in OT theory, which enables the application of ML tools.
The research project has broader societal impacts as it lays the foundations for uncertainty-aware autonomous systems, leading to significant improvements in their safety and efficiency. Research highlights of our team include: peer-reviewed publications in International Conference on Machine Learning, 2024 (ICML), Annual Conference on Neural Information Processing Systems (NeurIPS), 2023, Student Outstanding paper award at IEEE Conference on Decision and Control (CDC), 2024, semi-plenary lecture at the 26th International Symposium on Mathematical Theory of Networks and Systems (MTNS) 2024. This research is supported by the NSF award (2318977).
Key Ideas
- Variational formulation of Bayes’ law where the conditional distribution is identified as the push-forward of an optimal transport map
- In contrast to the importance sampling particle filters, the variational method is likelihood free and perform well in high-dimensional situations when the likelihood is degenerate.
- The stochastic optimization formulation allows for the application of the ML tools. namely the expressiveness of neural networks and scalability of stochastic optimization algorithms.