Kernel embeddings of distributions have recently gained significant attention in the machine learning community as a data-driven technique for representing probability distributions. Broadly, these techniques enable efficient computation of expectations by representing integral operators as elements in a reproducing kernel Hilbert space. We apply these techniques to the area of stochastic optimal control theory and present a method to compute approximately optimal policies for stochastic systems with arbitrary disturbances. Our approach reduces the optimization problem to a linear program, which can easily be solved via the Lagrangian dual, without resorting to gradient-based optimization algorithms. We focus on discrete-time dynamic programming, and demonstrate our proposed approach on a linear regulation problem, and on a nonlinear target tracking problem. This approach is broadly applicable to a wide variety of optimal control problems, and provides a means of working with stochastic systems in a data-driven setting.
A semidefinite program for least distortion embeddings of flat tori into Hilbert spaces
A. Heimendahl, M. L\"ucke, F. Vallentin, M.C. Zimmermann, Department Mathematik/Informatik, Abteilung Mathematik, Universit\"at zu K\"oln, Weyertal 86--90, 50931 K\"oln, Germany
Approximate Controllability of Nonlocal Stochastic Integrodifferential System in Hilbert Spaces
Université Gaston Berger de Saint-Louis（圣路易加斯顿·贝热大学）；PSG College of Arts & Science（PSG文理学院）；Virginia Military Institute (VMI)（弗吉尼亚军事学院）；UMMISCO UMI 209 IRD/UPMC（IRD/UPMC UMMISCO UMI 209）
Stochastic Bounded Real Lemma and $H_{\infty}$ Control of Difference Systems in Hilbert Spaces
School of Mathematics and Statistics, Shandong Normal University（山东师范大学数学与统计学院）；College of Electrical Engineering and Automation, Shandong University of Science and Technology（山东科技大学电气工程学院自动化）；School of Automation Science and Engineering, South China University of Technology（华南理工大学自动化科学与工程学院）
