# Toric Geometry of Entropic Regularization

arXiv: https://arxiv.org/abs/2202.01571 · HTML: https://mlsanity.com/paper/2202.01571/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 23 references that are in the map.
- First posted on arXiv 3 Feb 2022.

## Builds on (most cited first, 8 of 8)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures](https://mlsanity.com/paper/1508.07941/) (2015)
- [An explicit analysis of the entropic penalty in linear programming](https://mlsanity.com/paper/1806.01879/) (2018)
- [Generalized Sinkhorn iterations for regularizing inverse problems using optimal mass transport](https://mlsanity.com/paper/1612.02273/) (2016)
- [Computational Methods for Martingale Optimal Transport problems](https://mlsanity.com/paper/1710.07911/) (2017)
- [Iterative proportional scaling revisited: a modern optimization perspective](https://mlsanity.com/paper/1610.02588/) (2016)
- [Log-barrier interior point methods are not strongly polynomial](https://mlsanity.com/paper/1708.01544/) (2017)
- [The tropicalization of the entropic barrier](https://mlsanity.com/paper/2010.10205/) (2020)

## Built on by (most cited first, 1 of 1)

- [Fisher-Rao Gradient Flows of Linear Programs and State-Action Natural Policy Gradients](https://mlsanity.com/paper/2403.19448/) (2024)

## 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.