Abstract Human free-hand sketches have been studied in various contexts including sketch recognition, synthesis and finegrained sketch-based image retrieval (FG-SBIR). A fundamental challenge for sketch analysis is to deal with drastically different human drawing styles, particularly in terms of abstraction level. In this work, we propose the first stroke-level sketch abstraction model based on the insight of sketch abstraction as a process of trading off between the recognizability of a sketch and the number of strokes used to draw it. Concretely, we train a model for abstract sketch generation through reinforcement learning of a stroke removal policy that learns to predict which strokes can be safely removed without affecting recognizability. We show that our abstraction model can be used for various sketch analysis tasks including: (1) modeling stroke saliency and understanding the decision of sketch recognition models, (2) synthesizing sketches of variable abstraction for a given category, or reference object instance in a photo, and (3) training a FG-SBIR model with photos only, bypassing the expensive photo-sketch pair collection step