REVIEW 1 cited by
Sinkhorn Algorithm as a Special Case of Stochastic Mirror Descent
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original 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.
Forward citations
Cited by 1 Pith paper
-
Designing Algorithms for Entropic Optimal Transport from an Optimisation Perspective
A new Phi-match framework generalizes Sinkhorn and semi-dual gradient ascent for entropic OT, with O(1/N) and O(1/N^2) rates for several variants, plus a path-space Schrodinger bridge extension.
Discussion (0). Continue with ORCID to comment.