Toric Geometry of Entropic Regularization
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Abstract (arXiv)
Entropic regularization is a method for large-scale linear programming. Geometrically, one traces intersections of the feasible polytope with scaled toric varieties, starting at the Birch point. We compare this to log-barrier methods, with reciprocal linear spaces, starting at the analytic center. We revisit entropic regularization for unbalanced optimal transport, and we develop the use of optimal conic couplings. We compute the degree of the associated toric variety, and we explore algorithms like iterative scaling.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 8 of its 23 references that are in the map. First posted on arXiv 3 Feb 2022.
Builds on
8 of 23 references.
References · 8
- 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
- 2015Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measurescited by 138
- 2018An explicit analysis of the entropic penalty in linear programmingcited by 23
- 2016Generalized Sinkhorn iterations for regularizing inverse problems using optimal mass transportcited by 7
- 2017Computational Methods for Martingale Optimal Transport problemscited by 6
- 2016Iterative proportional scaling revisited: a modern optimization perspectivecited by 1
- 2017Log-barrier interior point methods are not strongly polynomialcited by 1
- 2020The tropicalization of the entropic barriercited by 1
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Citing papers per year: 2024: 1.
1 paper.