Summary: Improved Sample Complexity Estimates for Statistical Learning
Control of Uncertain Systems
V. Koltchinskii # , C. T. Abdallah + , M. Ariola # , P. Dorato § , D. Panchenko ¶
Recently, probabilistic methods and statistical learning theory have been shown to provide approximate
solutions to ``di#cult'' control problems. Unfortunately, the number of samples required in order to
guarantee stringent performance levels may be prohibitively large. This paper introduces bootstrap
learning methods and the concept of stopping times to drastically reduce the bound on the number of
samples required to achieve a performance level. We then apply these results to obtain more e#cient
algorithms which probabilistically guarantee stability and robustness levels when designing controllers
for uncertain systems.
keywords: Statistical Learning, Radamacher bootstrap, Robust Control, Sample Complexity, NPhard
problems, Decidability theory.
# V. Koltchinskii is with the Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131,
USA. Email: firstname.lastname@example.org. His research is partially supported by NSA Grant MDA9049910031
+ Corresponding Author: C. T. Abdallah is with the Department of EECE, University of New Mexico, Albuquerque, NM
87131, USA. Email: email@example.com. His research is partially supported by Boeing Computer Services Grant 348181,
and by NSF INT9818312
# M. Ariola is with the Dipartimento di Informatica e Sistemistica, Universit‘a degli Studi di Napoli Federico II, Napoli, Italy.
Email: firstname.lastname@example.org. His research is partially supported by the MURST