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Summary: IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 45, NO. 12, DECEMBER 2000 2383
Improved Sample Complexity Estimates for Statistical
Learning Control of Uncertain Systems
V. Koltchinskii, C. T. Abdallah, M. Ariola, P. Dorato, and
D. Panchenko
Abstract--Recently, probabilistic methods and statistical learning theory
have been shown to provide approximate solutions to "difficult" control
problems. Unfortunately, the number of samples required in order to guar-
antee 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 efficient al-
gorithms which probabilistically guarantee stability and robustness levels
when designing controllers for uncertain systems.
Index Terms--Decidability theory, -hard problems, Radamacher
bootstrap, robust control, sample complexity, statistical learning.
I. INTRODUCTION
It has recently become clear that many control problems are too diffi-
cult to admit analytic solutions [1], [2]. New results have also emerged
to show that the computational complexity of some "solved" control
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