Talk:Entropic Regularization

Entropic Regularization

• The title ``entropic regularization`` for this first section is not very descriptive; consider something like ``discretization of Kantorovich problem`` and reference the OT wiki page on discrete optimal transport
• Consider writing ``Due to the LINEAR structure of the Kantorovich problem``
• Change the label ``Kantorovich problem`` to link to the corresponding page on the wiki
• Consider specifying that ai, bj, xi, yj are real numbers, elements of Rn, etc
• Define the cost function; what assumptions are you imposing on the cost function? (possibly referencing the page on the Kantorovich problem)

The Entropic Regularization

• This section needs to be better distinguished from Santambrogio's book, so that it is not copyright infringement. Below are some ideas of things you can add/change to better distinguish it. Consider looking at the Peyre Cuturi book to learn more about entropic regularization.
• Why do we want to study this variant? (Hint: it has to due with convexity)
• Instead of ``tackling``, perhaps ``solving the Entropic regularized problem``, putting the reference to Santambrogio's book after the word ``problem``
• It's a little ambiguous what it meant by ``converges as eps to zero``. Perhaps clarify this (in a way different from Santabrogio) or remove this comment.
• There is a type-o with \textbf{KL}
• Change the phrase ``Kullback-Leibler`` to be a link to the corresponding wikipedia page.
• Add a sentence explaining why this constraint set enforces alphaij nonnegative (in a way different from S.)
• The last two paragraphs of this section are nearly identical to Santambrogio. Can you supplement with information from another reference to better distinguish your article?

Algorithm

• This section is too similar to Santambrogio and should be removed or rewritten. Perhaps replace this section with a section discussing the notion of convergence as epsilon to 0, since this section is really a duplicate of the other OT wiki article on Sinkhorn's algorithm

References

• There is a type-o in the references section