Pierre-Cyril Aubin-Frankowski (Mines ParisTech)
Tuesday, October 13th, 14h
Linear-Quadratic Optimal Control as a Kernel Regression with Hard Shape Constraints
Regression problems in control or machine learning typically involve shape constraints, such as positivity or monotonicity on a prescribed compact set. Such constraints stem from qualitative priors or physical constraints, and can often be written as an infinite number of pointwise inequalities. In the context of optimization over reproducing kernel Hilbert spaces of smooth functions, I will describe how to solve a strengthened problem with a finite number of second-order cone constraints and compute a priori and a posteriori bounds. This approach relies on coverings of compact sets in Hilbert spaces. It has been applied to non-crossing joint quantile regression, to Engel’s law in economics and to analyze or reconstruct vehicle trajectories. The second part of the talk will be devoted to applying this method to tackle linear-quadratic optimal control problems with state constraints. This leads to revisiting notions such as Gramians through the kernel lens.
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