19 citations · 25 across the 7 of their papers we have counts for
7 papers
Deep Learning as the Disciplined Construction of Tame Objects
Gilles Bareilles, Allen Gehret, Johannes Aspman +2
One can see deep-learning models as compositions of functions within the so-called tame geometry. In this expository note, we give an overview of some topics at the interface of ta…
Piecewise Polynomial Regression of Tame Functions via Integer Programming
Gilles Bareilles, Johannes Aspman, Jiri Nemecek +1
Tame functions are a class of nonsmooth, nonconvex functions, which feature in a wide range of applications: functions encountered in the training of deep neural networks with all…
Hybrid Methods in Polynomial Optimisation
Johannes Aspman, Gilles Bareilles, Vyacheslav Kungurtsev +2
The Moment/Sum-of-squares hierarchy provides a way to compute the global minimizers of polynomial optimization problems (POP), at the cost of solving a sequence of increasingly lar…
Harnessing structure in composite nonsmooth minimization
Gilles Bareilles, Franck Iutzeler, Jérôme Malick
We consider the problem of minimizing the composition of a nonsmooth function with a smooth mapping in the case where the proximity operator of the nonsmooth function can be explic…
Newton acceleration on manifolds identified by proximal-gradient methods
Gilles Bareilles, Franck Iutzeler, Jérôme Malick
Proximal methods are known to identify the underlying substructure of nonsmooth optimization problems. Even more, in many interesting situations, the output of a proximity operator…
Randomized Progressive Hedging methods for Multi-stage Stochastic Programming
Gilles Bareilles, Yassine Laguel, Dmitry Grishchenko +2
Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is that all scenario…
On the Interplay between Acceleration and Identification for the Proximal Gradient algorithm
Gilles Bareilles, Franck Iutzeler
In this paper, we study the interplay between acceleration and structure identification for the proximal gradient algorithm. We report and analyze several cases where this interpla…