sRecently, 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 he 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.