Improved Sample Complexity Estimates for Statistical Learning Control of Uncertain Systems

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 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 efficient algorithms which probabilistically guarantee stability and robustness levels when designing controllers for uncertain systems. Index Terms-Decidability theory, NP-hard problems, Radamacher bootstrap, robust control, sample complexity, statistical learning.