Title :
Revisiting statistical learning theory for uncertain feasibility and optimization problems
Author :
Alamo, T. ; Tempo, R. ; Camacho, E.F.
Author_Institution :
Sevilla Univ., Sevilla
Abstract :
In this paper, we study two general semi-infinite programming problems by means of statistical learning theory. The sample size results obtained with this approach are generally considered to be very conservative by the control community. The main contribution of this paper is to demonstrate that this is not necessarily the case. Using as a starting point one-side results from statistical learning theory, we obtain bounds on the number of required samples that are manageable for "reasonable" values of confidence delta and accuracy isin. In particular, we provide sample size bounds growing with 1/isin ln 1/isin instead of the usual 1/isin2 ln 1/isin2 dependence.
Keywords :
control system synthesis; learning (artificial intelligence); optimisation; statistical analysis; uncertain systems; optimization problems; semiinfinite programming problems; statistical learning theory; uncertain feasibility; Computational complexity; Control design; Control theory; Robust control; Robustness; Size control; Statistical learning; USA Councils; Uncertain systems; Uncertainty; Randomized algorithms; probabilistic robustness; robust convex optimization; statistical leaning theory; uncertain systems;
Conference_Titel :
Decision and Control, 2007 46th IEEE Conference on
Conference_Location :
New Orleans, LA
Print_ISBN :
978-1-4244-1497-0
Electronic_ISBN :
0191-2216
DOI :
10.1109/CDC.2007.4434625