Certification Aspects of the Fast Gradient Method for Solving the Dual of Parametric Convex Programs

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

This paper investigates the fundamental regression task of learning k neurons (a.k.a. teachers) from Gaussian input, using two-layer ReLU neural networks with width m (a.k.a. students) and m, k = O(1), trained via gradient descent under proper initializati ...

This work considers the low-rank approximation of a matrix (Formula presented.) depending on a parameter (Formula presented.) in a compact set (Formula presented.). Application areas that give rise to such problems include computational statistics and dyna ...

For a high-dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in terms of both computational cost and numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g., to the ge ...

Modern optimization is tasked with handling applications of increasingly large scale, chiefly due to the massive amounts of widely available data and the ever-growing reach of Machine Learning. Consequently, this area of research is under steady pressure t ...

We consider the problem of defining and fitting models of autoregressive time series of probability distributions on a compact interval of Double-struck capital R. An order-1 autoregressive model in this context is to be understood as a Markov chain, where ...

Distributed learning is the key for enabling training of modern large-scale machine learning models, through parallelising the learning process. Collaborative learning is essential for learning from privacy-sensitive data that is distributed across various ...

In light of the challenges posed by climate change and the goals of the Paris Agreement, electricity generation is shifting to a more renewable and decentralized pattern, while the operation of systems like buildings is increasingly electrified. This calls ...

We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of optimal control problems (OCPs) constrained by random partial differential equ ...

Driven by the need for more efficient and seamless integration of physical models and data, physics -informed neural networks (PINNs) have seen a surge of interest in recent years. However, ensuring the reliability of their convergence and accuracy remains ...

Within the context of contemporary machine learning problems, efficiency of optimization process depends on the properties of the model and the nature of the data available, which poses a significant problem as the complexity of either increases ad infinit ...

We present a framework for performing regression when both covariate and response are probability distributions on a compact and convex subset of

\R^d

. Our regression model is based on the theory of optimal transport and links the conditional Fr'echet m ...

In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence analysis of collective ...

This paper presents a theoretical analysis of linear interpolation as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss lan ...

Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...

Niobium nitride (NbN) is a particularly promising material for quantum technology applications, as it shows the degree of reproducibility necessary for large-scale superconducting circuits. We demonstrate that resonators based on NbN thin films present a o ...

We address black-box convex optimization problems, where the objective and constraint functions are not explicitly known but can be sampled within the feasible set. The challenge is thus to generate a sequence of feasible points converging towards an optim ...

Control design for robotic systems is complex and often requires solving an optimization to follow a trajectory accurately. Online optimization approaches like Model Predictive Control (MPC) have been shown to achieve great tracking performance, but requir ...

Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by using kernel me ...

Deep neural networks (DNN) have become an essential tool to tackle challenging tasks in many fields of computer science. However, their high computational complexity limits their applicability. Specialized DNN accelerators have been developed to accommodat ...

Sylvester matrix equations are ubiquitous in scientific computing. However, few solution techniques exist for their generalized multiterm version, as they now arise in an increasingly large number of applications. In this work, we consider algebraic parame ...

Certification Aspects of the Fast Gradient Method for Solving the Dual of Parametric Convex Programs

Chat with Graph Search

How Gradient Descent Balances Features: A Dynamical Analysis For Two-Layer Neural Networks

Randomized low-rank approximation of parameter-dependent matrices

Randomized flexible GMRES with deflated restarting

Scalable constrained optimization

On distributional autoregression and iterated transportation

Optimization Algorithms for Decentralized, Distributed and Collaborative Machine Learning

Quantifying the Unknown: Data-Driven Approaches and Applications in Energy Systems

A Combination Technique for Optimal Control Problems Constrained by Random PDEs

Residual-based attention in physics-informed neural networks

Universal and adaptive methods for robust stochastic optimization

Distributional Regression and Autoregression via Optimal Transport

A multigrid method for PDE-constrained optimization with uncertain inputs

Stable Nonconvex-Nonconcave Training via Linear Interpolation

Augmented Lagrangian Methods for Provable and Scalable Machine Learning

NbN films with high kinetic inductance for high-quality compact superconducting resonators

Safe Zeroth-Order Convex Optimization Using Quadratic Local Approximations

Training Efficient Controllers via Analytic Policy Gradient

Learning ground states of gapped quantum Hamiltonians with Kernel Methods

Hardware-Software Co-design for Improved Resource Utilization in DNN Accelerators

Preconditioning techniques for generalized Sylvester matrix equations