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Abstract: the paper introduces LearnSDD an algorithm that learns log-linear models for discrete random variables but adds a penalty term for models that are expensive at query time. Compared to earlier work in this direction the paper studies a new way of describing models (SDDs instead of ACs) and is interested in "complex queries", e.g. The computational complexity of complex queries are not directly addressed in the algorithm, but as it turns out the choice of SDD as model space also has good run-time performance for certain complex queries (Theorem 1). Quality: there are no obvious errors, but some definitions in the proof are missing. Some key elements in the algorithm are not motivated/discussed (see comments below) Clarity: The presentation is good enough, but can be improved.