A Gradient Descent Perspective on Sinkhorn

By Flavien Léger. Applied Mathematics and Optimization, 2020

51 citations recorded by the source corpus.

We present a new perspective on the popular Sinkhorn algorithm, showing that it can be seen as a Bregman gradient descent (mirror descent) of a relative entropy (Kullback–Leibler divergence). This viewpoint implies a new sublinear convergence rate with a robust constant.

Subfields: Applied Mathematics, Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/448f58cc6ae35539db0f30b36c07ca129981f95a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Arnaud Doucet
2. James Thornton
3. Jeremy Heng
4. Valentin De Bortoli
5. Marco Cuturi
6. G. Peyr'e
7. Victor M. Panaretos
8. Yoav Zemel

In Computational Mechanics

1. Arnaud Doucet
2. James Thornton
3. Jeremy Heng
4. Valentin De Bortoli

In Statistical and Nonlinear Physics

1. Arnaud Doucet
2. James Thornton
3. Jeremy Heng
4. Valentin De Bortoli

Citations in the corpus

• Diffusion Schrödinger Bridge with Applications to Score-Based Generative Modeling (2021, methodology): “Additionally, we derive novel quantitative convergence results for IPF in continuous state-space which do not rely on classical compactness assumptions (Chen et al., 2016; Ruschendorf et al., 1995) and improve on the recent results of Léger (2020).”