We propose an approach to learning from demonstration (LfD) which leverages expert data, even if the expert examples are very few or inaccurate. We achieve this by integrating LfD in an approximate policy iteration algorithm. The key idea of our approach is that expert examples are used to generate linear constraints on the optimization, in a similar fashion to large-margin classification. We prove an upper bound on the true Bellman error of the approximation computed by the algorithm at each iteration. We show empirically that the algorithm outperforms both pure policy iteration, as well as DAgger (a state-of-art LfD algorithm) and supervised learning in a variety of scenarios, including when very few and/or imperfect demonstrations are available. Our experiments include simulations as well as a real robotic navigation task.