Conditional preference networks (CP-nets) provide a powerful, compact, and intuitive graphical tool to represent the preferences of a user. However learning such a structure is known to be a difficult problem due to its combinatorial nature. We propose in this paper a new, efficient, and robust query-based learning algorithm for acyclic CP-nets. In particular, our algorithm takes into account the incoherences in the user's preferences or in noisy data by searching in a principled way the variables that condition the other ones. We provide complexity results of the algorithm, and demonstrate its efficiency through an empirical evaluation on synthetic and on real datasets.