This paper presents a framework for the theoretical analysis of Estimation of Distribution Algorithms (EDA). Using this framework, derived from the VC-theory, we propose non-asymptotic bounds which depend on: 1) the population size 2) the selection rate, 3) the families of distributions used for the modelling, 4) the dimension, and 5) the number of iterations. To validate these results, optimization algorithms are applied to a context where bounds on resources are crucial, namely Design of Experiments, that is a black-box optimization with very few fitness-values evaluations.