Capture, Propagate, and Control Distributional Uncertainty
Event details
| Date | 30.06.2023 |
| Hour | 11:00 › 12:00 |
| Speaker | Liviu Aolaritei (ETH Zürich) |
| Location | |
| Category | Conferences - Seminars |
| Event Language | English |
Abstract:
Uncertainty propagation has established itself as a fundamental area of research in all fields of science and engineering. Among its central topics stands the problem of modeling and propagating distributional uncertainty, i.e., uncertainty about probability distributions. In this talk, we employ tools from Optimal Transport (OT) to capture distributional uncertainty via OT ambiguity sets, which we show to be very natural and expressive, and to enjoy powerful geometrical, computational, and statistical features and guarantees. We show that these ambiguity sets propagate nicely and intuitively through linear and nonlinear (possibly corrupted by stochastic noise) transformations, and that in many cases the result of the propagation is again an OT ambiguity set. Moreover, whenever this is not the case, we show that the result of the propagation can be tightly upper bounded by another OT ambiguity set.
We then specialize our results to stochastic LTI systems where only partial statistical information about the noise is available (e.g., samples), and start by showing that distributional uncertainty can be efficiently captured, with high probability, within an OT ambiguity set on the space of noise trajectories. Then, we show that such ambiguity sets propagate exactly through the system dynamics, giving rise to stochastic tubes that contain, with high probability, all trajectories of the stochastic system. Finally, we show that the control task is very interpretable, unveiling an interesting decomposition between the roles of the feedforward and the feedback control terms. This theory is successfully exploited to formulate a Wasserstein Tube MPC capable of optimally trading between safety and performance.
Bio:
Liviu Aolaritei is a PhD student in the Automatic Control Lab at ETH Zürich. Prior to his PhD, he received a Master Degree in Robotics, Systems, and Control from ETH Zürich, and a Bachelor Degree in Information Engineering from the University of Padova. During his PhD he was a visiting graduate student in the Operations Research Center at MIT, and in the IEOR Department at Columbia University. His current research interests revolve around Distributionally Robust Optimization and Optimal Transport, as well as their application in Automatic Control, Machine Learning, Operations Research, and Energy Systems.
Uncertainty propagation has established itself as a fundamental area of research in all fields of science and engineering. Among its central topics stands the problem of modeling and propagating distributional uncertainty, i.e., uncertainty about probability distributions. In this talk, we employ tools from Optimal Transport (OT) to capture distributional uncertainty via OT ambiguity sets, which we show to be very natural and expressive, and to enjoy powerful geometrical, computational, and statistical features and guarantees. We show that these ambiguity sets propagate nicely and intuitively through linear and nonlinear (possibly corrupted by stochastic noise) transformations, and that in many cases the result of the propagation is again an OT ambiguity set. Moreover, whenever this is not the case, we show that the result of the propagation can be tightly upper bounded by another OT ambiguity set.
We then specialize our results to stochastic LTI systems where only partial statistical information about the noise is available (e.g., samples), and start by showing that distributional uncertainty can be efficiently captured, with high probability, within an OT ambiguity set on the space of noise trajectories. Then, we show that such ambiguity sets propagate exactly through the system dynamics, giving rise to stochastic tubes that contain, with high probability, all trajectories of the stochastic system. Finally, we show that the control task is very interpretable, unveiling an interesting decomposition between the roles of the feedforward and the feedback control terms. This theory is successfully exploited to formulate a Wasserstein Tube MPC capable of optimally trading between safety and performance.
Bio:
Liviu Aolaritei is a PhD student in the Automatic Control Lab at ETH Zürich. Prior to his PhD, he received a Master Degree in Robotics, Systems, and Control from ETH Zürich, and a Bachelor Degree in Information Engineering from the University of Padova. During his PhD he was a visiting graduate student in the Operations Research Center at MIT, and in the IEOR Department at Columbia University. His current research interests revolve around Distributionally Robust Optimization and Optimal Transport, as well as their application in Automatic Control, Machine Learning, Operations Research, and Energy Systems.
Practical information
- General public
- Free