5 citations · 17 across the 22 of their papers we have counts for
23 papers
Fenchel-Young Duality Gaps: Certified Early Stopping for Regularized Inverse Problems
Pierre-Cyril Aubin-Frankowski, Yohann de Castro
We study computable error bounds and certified early stopping for regularized inverse problems, where a data-fidelity term is traded against a regularizer. The analysis relies on a…
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…
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 debiasa…
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…
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…
Mirror and Preconditioned Gradient Descent in Wasserstein Space
Clément Bonet, Théo Uscidda, Adam David +2
As the problem of minimizing functionals on the Wasserstein space encompasses many applications in machine learning, different optimization algorithms on have receiv…
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…
Reproducing kernel approach to linear quadratic mean field control problems
Pierre-Cyril Aubin-Frankowski, Alain Bensoussan
Mean-field control problems have received continuous interest over the last decade. Despite being more intricate than in classical optimal control, the linear-quadratic setting can…
Alternating minimization for simultaneous estimation of a latent variable and identification of a linear continuous-time dynamic system
Pierre-Cyril Aubin-Frankowski, Alain Bensoussan, S. Joe Qin
We propose an optimization formulation for the simultaneous estimation of a latent variable and the identification of a linear continuous-time dynamic system, given a single input-…
Gradient descent with a general cost
Flavien Léger, Pierre-Cyril Aubin-Frankowski
We present a new class of gradient-type optimization methods that extends vanilla gradient descent, mirror descent, Riemannian gradient descent, and natural gradient descent. Our a…
Approximation of optimization problems with constraints through kernel Sum-Of-Squares
Pierre-Cyril Aubin-Frankowski, Alessandro Rudi
Handling an infinite number of inequality constraints in infinite-dimensional spaces occurs in many fields, from global optimization to optimal transport. These problems have been…
The reproducing kernel Hilbert spaces underlying linear SDE Estimation, Kalman filtering and their relation to optimal control
Pierre-Cyril Aubin-Frankowski, Alain Bensoussan
It is often said that control and estimation problems are in duality. Recently, in (Aubin-Frankowski,2021), we found new reproducing kernels in Linear-Quadratic optimal control by…
Stability of solutions for controlled nonlinear systems under perturbation of state constraints
Pierre-Cyril Aubin-Frankowski
This paper tackles the problem of nonlinear systems, with sublinear growth but unbounded control, under perturbation of some time-varying state constraints. It is shown that, given…
Operator-valued Kernels and Control of Infinite dimensional Dynamic Systems
Pierre-Cyril Aubin-Frankowski, Alain Bensoussan
The Linear Quadratic Regulator (LQR), which is arguably the most classical problem in control theory, was recently related to kernel methods in (Aubin-Frankowski, SICON, 2021) for…
Mirror Descent with Relative Smoothness in Measure Spaces, with application to Sinkhorn and EM
Pierre-Cyril Aubin-Frankowski, Anna Korba, Flavien Léger
Many problems in machine learning can be formulated as optimizing a convex functional over a vector space of measures. This paper studies the convergence of the mirror descent algo…
Tropical reproducing kernels and optimization
Pierre-Cyril Aubin-Frankowski, Stéphane Gaubert
Hilbertian kernel methods and their positive semidefinite kernels have been extensively used in various fields of applied mathematics and machine learning, owing to their several e…
Kernel Stein Discrepancy Descent
Anna Korba, Pierre-Cyril Aubin-Frankowski, Szymon Majewski +1
Among dissimilarities between probability distributions, the Kernel Stein Discrepancy (KSD) has received much interest recently. We investigate the properties of its Wasserstein gr…
Handling Hard Affine SDP Shape Constraints in RKHSs
Pierre-Cyril Aubin-Frankowski, Zoltan Szabo
Shape constraints, such as non-negativity, monotonicity, convexity or supermodularity, play a key role in various applications of machine learning and statistics. However, incorpor…
Interpreting the dual Riccati equation through the LQ reproducing kernel
Pierre-Cyril Aubin-Frankowski
In this study, we provide an interpretation of the dual differential Riccati equation of Linear-Quadratic (LQ) optimal control problems. Adopting a novel viewpoint, we show that LQ…
Linearly-constrained Linear Quadratic Regulator from the viewpoint of kernel methods
Pierre-Cyril Aubin-Frankowski
The linear quadratic regulator problem is central in optimal control and was investigated since the very beginning of control theory. Nevertheless, when it includes affine state co…
Hard Shape-Constrained Kernel Machines
Pierre-Cyril Aubin-Frankowski, Zoltan Szabo
Shape constraints (such as non-negativity, monotonicity, convexity) play a central role in a large number of applications, as they usually improve performance for small sample size…
Aronszajn's reproducing kernels and Feynman propagators
Pierre-Cyril Aubin-Frankowski
This study shows how Aronszajn's theory of reproducing kernels can be of use for the construction the Hilbert spaces of quantum theory. We show that the Feynman propagator is an ex…