Bregman Projections over Submodular Base Polytopes
نویسندگان
چکیده
A well-known computational bottleneck in various first order methods like mirror descent is that of computing a certain Bregman projection. We give a novel algorithm, INC-FIX, for computing these projections under separable mirror maps and more generally for minimizing separable convex functions over submodular base polytopes. For minimizing divergences onto cardinality-based submodular base polytopes defined on ground set E, we prove an O(|E|) running time under any uniformly separable mirror map. This matches the running time of [9, 13] for projections under KL-divergence and squared Euclidean distance, recovers an algorithm from [16] for computing projections over the simplex.
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