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)

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?

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