9 papers
Langevin for Nonconvex Optimization: Exact, Inexact and Zeroth-Order
Emanuele Naldi, Marco Rando, Lorenzo Rosasco +1
We study Langevin-based methods for non-convex optimization under smoothness and dissipativity assumptions. Our focus is on obtaining non-asymptotic bounds for the expected excess…
On the stability of proximal operators in Wasserstein spaces under different notions of convexity
Simone Di Marino, Sara Farinelli, Emanuele Naldi
The proximal operator is a fundamental tool in variational analysis and optimization. In the setting of a Hilbert space, given a proper, lower semicontinuous convex functional, its…
Convergence of zeroth-order proximal point algorithms in the high-temperature regime
Emanuele Naldi, Hippolyte Labarrière, Cesare Molinari +1
Efficient methods for non-convex black-box optimization largely rely on sampling. In this context, the Zeroth-Order Proximal Operator (ZOPO) and the corresponding Zeroth-Order Prox…
A Lipschitz spaces view of infinitely wide shallow neural networks
Francesca Bartolucci, Marcello Carioni, José A. Iglesias +3
We revisit the mean field parametrization of shallow neural networks, using signed measures on unbounded parameter spaces and duality pairings that take into account the regularity…
The Influence of an Adjoint Mismatch on the Primal-Dual Douglas-Rachford Method
Emanuele Naldi, Felix Schneppe
The primal-dual Douglas-Rachford method is a well-known algorithm to solve optimization problems written as convex-concave saddle-point problems. Each iteration involves solving a…
Learning Firmly Nonexpansive Operators
Kristian Bredies, Jonathan Chirinos-Rodriguez, Emanuele Naldi
This paper proposes a data-driven approach for constructing firmly nonexpansive operators. We demonstrate its applicability in Plug-and-Play (PnP) methods, where classical algorith…