12 citations · 24 across the 24 of their papers we have counts for
27 papers
Optimization by Reparametrization: Time-Warped Mirror Flows with Singular Geometry
Cristian Vega, Cesare Molinari, Lorenzo Rosasco +1
Solving data-driven problems requires defining complex models and fitting them to data, neural networks being a motivating example. The fitting procedure can be seen as an optimiza…
Learning to control switching nonlinear systems with Koopman operator regression
Edoardo Caldarelli, Oleksii Kachaiev, Cesare Molinari +1
In this work, we consider the identification and control of nonlinear systems with finite action spaces. The unknown dynamics are estimated from finite samples with Koopman operato…
Frank-Wolfe with Moreau Envelope Smoothing for Nonsmooth Nonconvex Problems
Antonio Silveti-Falls, Cesare Molinari, Zev Woodstock
We present and analyze Frank-Wolfe with Moreau Envelope Smoothing (FRAMES) for solving nonsmooth nonconvex constrained optimization problems, taking advantage of iterative smoothin…
Proximal basin hopping: global optimization with guarantees
Guillaume Lauga, Cesare Molinari, Samuel Vaiter
Global optimization is a challenging problem, with plenty of algorithms displaying empirical success, but scarce theoretical backing. In this work, we propose a new theoretical fra…
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…
SGD for Variational Inference: Tackling Unbounded Variance via Preconditioning and Dynamic Batching
Hippolyte Labarrière, Cesare Molinari, Silvia Villa +1
Black-Box Variational Inference (BBVI) typically relies on Stochastic Gradient Descent (SGD) to optimize the Evidence Lower Bound (ELBO). However, the stochastic gradients in BBVI…
Existence and optimisation of the partial correlation graphical lasso
Jack Storror Carter, Cesare Molinari
The partial correlation graphical LASSO (PCGLASSO) is a penalised likelihood method for Gaussian graphical models which provides scale invariant sparse estimation of the precision…
A Proximal Stochastic Variance Reduced Zeroth-order Algorithm using Structured Finite-Differences
Marco Rando, Cheik Traoré, Cesare Molinari +2
Minimizing finite sums of functions is a central problem in optimization, arising in numerous practical applications. Such problems are commonly addressed using first-order optimiz…
Preconditioned primal-dual dynamics in convex optimization: non-ergodic convergence rates
Vassilis Apidopoulos, Cesare Molinari, Juan Peypouquet +1
We introduce and analyze a continuous primal-dual dynamical system in the context of the minimization problem , where and are convex functions and is a line…
A Structured Tour of Optimization with Finite Differences
Marco Rando, Cesare Molinari, Lorenzo Rosasco +1
Finite-difference methods are widely used for zeroth-order optimization in settings where gradient information is unavailable or expensive to compute. These procedures mimic first-…
Model Consistency of the Iterative Regularization of Dual Ascent for Low-Complexity Regularization
Jie Gao, Cesare Molinari, Silvia Villa +1
Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include varia…
Optimization Insights into Deep Diagonal Linear Networks
Hippolyte Labarrière, Cesare Molinari, Lorenzo Rosasco +2
Gradient-based methods successfully train highly overparameterized models in practice, even though the associated optimization problems are markedly nonconvex. Understanding the me…
Automatic Gain Tuning for Humanoid Robots Walking Architectures Using Gradient-Free Optimization Techniques
Carlotta Sartore, Marco Rando, Giulio Romualdi +3
Developing sophisticated control architectures has endowed robots, particularly humanoid robots, with numerous capabilities. However, tuning these architectures remains a challengi…
Linear quadratic control of nonlinear systems with Koopman operator learning and the Nyström method
Edoardo Caldarelli, Antoine Chatalic, Adrià Colomé +4
In this paper, we study how the Koopman operator framework can be combined with kernel methods to effectively control nonlinear dynamical systems. While kernel methods have typical…
On Learning the Optimal Regularization Parameter in Inverse Problems
Jonathan Chirinos Rodriguez, Ernesto De Vito, Cesare Molinari +2
Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this chal…
Be greedy and learn: efficient and certified algorithms for parametrized optimal control problems
Hendrik Kleikamp, Martin Lazar, Cesare Molinari
We consider parametrized linear-quadratic optimal control problems and provide their online-efficient solutions by combining greedy reduced basis methods and machine learning algor…
Regularization properties of dual subgradient flow
Vassilis Apidopoulos, Cesare Molinari, Lorenzo Rosasco +1
Dual gradient descent combined with early stopping represents an efficient alternative to the Tikhonov variational approach when the regularizer is strongly convex. However, for ma…
An Optimal Structured Zeroth-order Algorithm for Non-smooth Optimization
Marco Rando, Cesare Molinari, Lorenzo Rosasco +1
Finite-difference methods are a class of algorithms designed to solve black-box optimization problems by approximating a gradient of the target function on a set of directions. In…
Stochastic Zeroth order Descent with Structured Directions
Marco Rando, Cesare Molinari, Silvia Villa +1
We introduce and analyze Structured Stochastic Zeroth order Descent (S-SZD), a finite difference approach that approximates a stochastic gradient on a set of orthogonal d…
Fast iterative regularization by reusing data
Cristian Vega, Cesare Molinari, Lorenzo Rosasco +1
Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to enforce uniqueness and select a meani…
Iterative regularization for low complexity regularizers
Cesare Molinari, Mathurin Massias, Lorenzo Rosasco +1
Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechani…
A Stochastic Bregman Primal-Dual Splitting Algorithm for Composite Optimization
Antonio Silveti-Falls, Cesare Molinari, Jalal Fadili
We study a stochastic first order primal-dual method for solving convex-concave saddle point problems over real reflexive Banach spaces using Bregman divergences and relative smoot…
Zeroth order optimization with orthogonal random directions
David Kozak, Cesare Molinari, Lorenzo Rosasco +2
We propose and analyze a randomized zeroth-order approach based on approximating the exact gradient byfinite differences computed in a set of orthogonal random directions that chan…
Iterative regularization for convex regularizers
Cesare Molinari, Mathurin Massias, Lorenzo Rosasco +1
We study iterative regularization for linear models, when the bias is convex but not necessarily strongly convex. We characterize the stability properties of a primal-dual gradient…