Abstract : It was shown recently that SVMs are particularly adequate to define action policies to keep a dynamical system inside a given constraint set (in the framework of viability theory). However, the training set size of the SVMs faces the dimensionality curse, because it is based on a regular grid of the state space. In this paper, we propose an active learning approach, aiming at decreasing dramatically the training set size, keeping it as close as possible to the final number of support vectors. We use a virtual multi-resolution grid, and some particularities of the problem, to choose very efficient examples to add to the training set. To illustrate the performances of the algorithm, we solve a six-dimensional problem, controlling a bike on a track, problem usually solved using reinforcement learning techniques.