In many applications, such as virtual agents or humanoid robots, it is difficult to represent complex human behaviors and the full range of skills necessary to achieve them. Real life human behaviors are often the combination of several parts and never reproduced in the exact same way. In this work we introduce a new algorithm that is able to learn behaviors by assuming that the observed complex motions can be represented in a smaller dictionary of concurrent tasks. We present an optimization formalism and show how we can learn simultaneously the dictionary and the mixture coefficients that represent each demonstration. We present results on a idealized model where a set of potential functions represents human objectives or preferences for achieving a task.