Statistical learning control of uncertain systems: theory and algorithms.
It is well known that control problems can be solved very seldomly exactly. On the other hand, many of the control problems can be reduced to decidability or optimization problems and, moreover, probabilistic methods (based on the Monte Carlo approach) can be employed to solve the new problems approximately. To obtain an accuracy of these methods, the Chernoff Bounds, the Hoeffding Inequality (or generally empirical processes and statistical learning theory) can be employed. However, it is known (from the literature) that a large number of the random samples can only (in this approach) guarantee the accuracy. The authors of the paper suggest another approach. They suggest bootstrap sequential learning algorithms based on Rademacher bootstrap (or other bootstrap techniques). A random number of samples (known as the sample complexity of learning) appears in such algorithms. The theoretical, ``underlying'' assertions are recalled here; however, their proofs can be found in a former paper of V. Koltchinskii, C. T. Adallah and M. Ariola. The introduced algorithm is illustrated on an example, already known from the literature. The paper is written in an understandable way.
scientific article; zbMATH DE number 1860862