dc.contributor.author Mishchenko, Konstantin dc.date.accessioned 2019-12-24T08:00:34Z dc.date.available 2019-12-24T08:00:34Z dc.date.issued 2019-09-16 dc.identifier.uri http://hdl.handle.net/10754/660769 dc.description.abstract We present a new perspective on the celebrated Sinkhorn algorithm by showing that is a special case of incremental/stochastic mirror descent. In order to see this, one should simply plug Kullback-Leibler divergence in both mirror map and the objective function. Since the problem has unbounded domain, the objective function is neither smooth nor it has bounded gradients. However, one can still approach the problem using the notion of relative smoothness, obtaining that the stochastic objective is 1-relative smooth. The discovered equivalence allows us to propose 1) new methods for optimal transport, 2) an extension of Sinkhorn algorithm beyond two constraints. dc.publisher arXiv dc.relation.url https://arxiv.org/pdf/1909.06918 dc.rights Archived with thanks to arXiv dc.title Sinkhorn Algorithm as a Special Case of Stochastic Mirror Descent dc.type Preprint dc.contributor.department Computer Science Program dc.eprint.version Pre-print dc.identifier.arxivid 1909.06918 kaust.person Mishchenko, Konstantin refterms.dateFOA 2019-12-24T08:01:05Z
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