Numerical Analysis and Scientific Computing Seminar | Dante Kalise, Data-driven schemes for Hamilton-Jacobi-Bellman equations

MC 5417 and Zoom (Please contact ddelreyfernandez@uwaterloo.ca for Zoom link) 

Speaker

Dante Kalise, Senior Lecturer in Computational Optimization and Control, Department of Mathematics, Imperial College London

Title

Data-driven schemes for Hamilton-Jacobi-Bellman equations

Abstract

Optimal feedback synthesis for nonlinear dynamics -a fundamental problem in optimal control- is enabled by solving fully nonlinear Hamilton-Jacobi-Bellman type PDEs arising in dynamic programming. While our theoretical understanding of dynamic programming and HJB PDEs has seen a remarkable development over the last decades, the numerical approximation of HJB-based feedback laws has remained largely an open problem due to the curse of dimensionality. More precisely, the associated HJB PDE must be solved over the state space of the dynamics, which is extremely high-dimensional in applications such as distributed parameter systems or agent-based models. In this talk we will review recent approaches regarding the effective numerical approximation of very high-dimensional HJB PDEs. We will explore modern scientific computing methods based on tensor decompositions of the value function of the control problem, and the construction of data-driven schemes in supervised, and semi-supervised learning environments. We will highlight some novel research directions at the intersection of control theory, scientific computing, and statistical machine learning.