6 papers
Debiasing optimal transport: classical and entropic
Pierre-Cyril Aubin-Frankowski, Virginie Ehrlacher, Gabriele Todeschi
We study the notion of debiasability for cost functions arising in optimal transport. We call a symmetric cost function …
Difference of Convex Programming in the Wasserstein Space with Applications to MMD Optimization
Clément Bonet, Pierre-Cyril Aubin-Frankowski, Youssef Mroueh
Optimizing functionals over the space of probability measures is now ubiquitous in machine learning. A widely used approach is to perform the optimization directly over the Wassers…
The Brezis-Ekeland-Nayroles principle in metric spaces: time-continuous setting
Pierre-Cyril Aubin-Frankowski, Giacomo Enrico Sodini, Ulisse Stefanelli
Based on a variational characterization of the local slope of a functional, we extend the celebrated Brezis-Ekeland-Nayroles null-minimization principle to curves of maximal slope…
Generalization Bounds of Surrogate Policies for Combinatorial Optimization Problems
Pierre-Cyril Aubin-Frankowski, Yohann De Castro, Axel Parmentier +1
Many real-world decision problems require solving, again and again, combinatorial optimization instances drawn from a common distribution. A recent line of structured learning meth…
Evolution variational inequalities with general costs
Pierre-Cyril Aubin-Frankowski, Giacomo Enrico Sodini, Ulisse Stefanelli
We extend the theory of gradient flows beyond metric spaces by studying evolution variational inequalities (EVIs) driven by general cost functions , including Bregman and entrop…
Order isomorphisms of sup-stable function spaces: continuous, Lipschitz, c-convex, and beyond
Pierre-Cyril Aubin-Frankowski, Stéphane Gaubert
There have been many parallel streams of research studying order isomorphisms of some specific sets of functions from a set to , such as the se…