Statistical learning theory: A pack-based strategy for uncertain feasibility and optimization problems

Abstract

In this paper, a new powerful technique, denoted as pack-based strategy is introduced in the context of statistical learning theory. This strategy allows us to derive bounds on the number of required samples that are manageable for "reasonable" values of probabilistic confidence and accuracy. Using this technique for feasibility and optimization problems involving Boolean expressions consisting of polynomials, we prove that the number of required samples grows with the accuracy parameter ε as . This is a significant improvement when compared to the existing bounds which depend on . We also apply this strategy to convex optimization problems. In this case, we show that the required sample size is inversely proportional to the accuracy for fixed confidence. © 2008 Springer London.