2 citations · 2 across the 12 of their papers we have counts for
14 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, focusing on non-asymptotic expected excess-risk bounds rather than sampl…
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…
Inexact JKO and proximal-gradient algorithms in the Wasserstein space
Simone Di Marino, Emanuele Naldi, Silvia Villa
This paper studies the convergence properties of the inexact Jordan-Kinderlehrer-Otto (JKO) scheme and proximal-gradient algorithm in the context of Wasserstein spaces. The JKO sch…
Splitting the Forward-Backward Algorithm: A Full Characterization
Anton Åkerman, Enis Chenchene, Pontus Giselsson +1
We study frugal splitting algorithms with minimal lifting for solving monotone inclusion problems involving sums of maximal monotone and cocoercive operators. Building on a foundat…
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…
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…
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…
A general framework for inexact splitting algorithms with relative errors and applications to Chambolle-Pock and Davis-Yin methods
M. Marques Alves, Dirk A. Lorenz, Emanuele Naldi
In this work we apply the recently introduced framework of degenerate preconditioned proximal point algorithms to the hybrid proximal extragradient (HPE) method for maximal monoton…
On extreme points and representer theorems for the Lipschitz unit ball on finite metric spaces
Kristian Bredies, Jonathan Chirinos Rodriguez, Emanuele Naldi
In this note, we provide a characterization for the set of extreme points of the Lipschitz unit ball in a specific vectorial setting. While the analysis of the case of real-valued…
The Degenerate Variable Metric Proximal Point Algorithm and Adaptive Stepsizes for Primal-Dual Douglas-Rachford
Dirk A. Lorenz, Jannis Marquardt, Emanuele Naldi
In this paper the degenerate preconditioned proximal point algorithm will be combined with the idea of varying preconditioners leading to the degenerate variable metric proximal po…
Graph and distributed extensions of the Douglas-Rachford method
Kristian Bredies, Enis Chenchene, Emanuele Naldi
In this paper, we propose several graph-based extensions of the Douglas-Rachford splitting (DRS) method to solve monotone inclusion problems involving the sum of maximal monoto…
Degenerate Preconditioned Proximal Point algorithms
Kristian Bredies, Enis Chenchene, Dirk A. Lorenz +1
In this paper we describe a systematic procedure to analyze the convergence of degenerate preconditioned proximal point algorithms. We establish weak convergence results under mild…
Weak topology and Opial property in Wasserstein spaces, with applications to Gradient Flows and Proximal Point Algorithms of geodesically convex functionals
Emanuele Naldi, Giuseppe Savaré
In this paper we discuss how to define an appropriate notion of weak topology in the Wasserstein space of Borel probability measures with finite quadratic…