Reviews: Geometric Descent Method for Convex Composite Minimization

Summary: The paper extends the recent work of Bubeck et al. on the geometric gradient descent method, in order to handle non-smooth (but "nice") objectives. Similar work can be found in [10]; however, no optimal rates are obtained in that case (in the sense of having a square root condition number in the retraction factor). The core ideas and motivation origin from the proximity operators used in non-smooth optimization in machine learning and signal processing (see e.g., lasso). Quality: The paper is of good technical quality - for clarity see below. The results could be considered "expected" since similar results (from smooth to non-smooth convex objectives with proximal operators) have been proved in numerous papers the past decade; especially under convexity assumptions.