We propose a non-parametric anomaly detection algorithm for high dimensional data. We first rank scores derived from nearest neighbor graphs on (n)-point nominal training data. We then train limited complexity models to imitate these scores based on the max-margin learning-to-rank framework. A test-point is declared as an anomaly at (\alpha)-false alarm level if the predicted score is in the (\alpha)-percentile. The resulting anomaly detector is shown to be asymptotically optimal in that for any false alarm rate (\alpha), its decision region converges to the (\alpha)-percentile minimum volume level set of the unknown underlying density. In addition, we test both the statistical performance and computational efficiency of our algorithm on a number of synthetic and real-data experiments. Our results demonstrate the superiority of our algorithm over existing (K)-NN based anomaly detection algorithms, with significant computational savings.