Access the full text.
Sign up today, get DeepDyve free for 14 days.
We introduce a new second order stochastic algorithm to estimate the entropically regularized optimal transport (OT) cost between two probability measures. The source measure can be arbitrary chosen, either absolutely continuous or discrete, whereas the target measure is assumed to be discrete. To solve the semi-dual formulation of such a regularized and semi-discrete optimal transportation problem, we propose to consider a stochastic Gauss–Newton (SGN) algorithm that uses a sequence of data sampled from the source measure. This algorithm is shown to be adaptive to the geometry of the underlying convex optimization problem with no important hyperparameter to be accurately tuned. We establish the almost sure convergence and the asymptotic normality of various estimators of interest that are constructed from this SGN algorithm. We also analyze their non-asymptotic rates of convergence for the expected quadratic risk in the absence of strong convexity of the underlying objective function. The results of numerical experiments from simulated data are also reported to illustrate the finite sample properties of this Gauss–Newton algorithm for stochastic regularized OT and to show its advantages over the use of the stochastic gradient descent, stochastic Newton and ADAM algorithms.
Information and Inference A Journal of the IMA – Oxford University Press
Published: May 19, 2022
Keywords: stochastic optimization; stochastic Gauss–Newton algorithm; optimal transport; entropic regularization; convergence of random variables
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.