Toric Geometry of Entropic Regularization
Optimization and Control
2023-02-13 v2 Machine Learning
Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.2202.01571,
title = {Toric Geometry of Entropic Regularization},
author = {Bernd Sturmfels and Simon Telen and François-Xavier Vialard and Max von Renesse},
journal= {arXiv preprint arXiv:2202.01571},
year = {2023}
}
Comments
17 pages