Accelerated And Inexact Forward-Backward Algorithms

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Publications associées (32)

Asymptotic Errors for Teacher-Student Convex Generalized Linear Models (Or: How to Prove Kabashima’s Replica Formula)

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There has been a recent surge of interest in the study of asymptotic reconstruction performance in various cases of generalized linear estimation problems in the teacher-student setting, especially for the case of i.i.d standard normal matrices. Here, we g ...

2022

Implicit Bias of SGD for Diagonal Linear Networks: a Provable Benefit of Stochasticity

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Understanding the implicit bias of training algorithms is of crucial importance in order to explain the success of overparametrised neural networks. In this paper, we study the dynamics of stochastic gradient descent over diagonal linear networks through i ...

2021

Last iterate convergence of SGD for Least-Squares in the Interpolation regime

Aditya Vardhan Varre, Nicolas Henri Bernard Flammarion, Loucas Pillaud-Vivien

Motivated by the recent successes of neural networks that have the ability to fit the data perfectly \emph{and} generalize well, we study the noiseless model in the fundamental least-squares setup. We assume that an optimum predictor fits perfectly inputs ...

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On the nonlinear Dirichlet-Neumann method and preconditioner for Newton's method

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The Dirichlet-Neumann (DN) method has been extensively studied for linear partial differential equations, while little attention has been devoted to the nonlinear case. In this paper, we analyze the DN method both as a nonlinear iterative method and as a p ...

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Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

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We consider the numerical approximation of an optimal control problem for an elliptic Partial Differential Equation (PDE) with random coefficients. Specifically, the control function is a deterministic, distributed forcing term that minimizes the expected ...

2021

Decentralized Proximal Gradient Algorithms With Linear Convergence Rates

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This article studies a class of nonsmooth decentralized multiagent optimization problems where the agents aim at minimizing a sum of local strongly-convex smooth components plus a common nonsmooth term. We propose a general primal-dual algorithmic framewor ...

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STORM+: Fully Adaptive SGD with Momentum for Nonconvex Optimization

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In this work we investigate stochastic non-convex optimization problems wherethe objective is an expectation over smooth loss functions, and the goal is to find an approximate stationary point. The most popular approach to handling such problems is varianc ...

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A Rosetta-based protein design protocol converging to natural sequences

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Computational protein design has emerged as a powerful tool capable of identifying sequences compatible with pre-defined protein structures. The sequence design protocols, implemented in the Rosetta suite, have become widely used in the protein engineering ...

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Data-Driven Convergence Prediction of Astrobots Swarms

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Astrobots are robotic artifacts whose swarms are used in astrophysical studies to generate the map of the observable universe. These swarms have to be coordinated with respect to various desired observations. Such coordination\footnote{\z{A coordination sa ...

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Adaptation in Stochastic Algorithms: From Nonsmooth Optimization to Min-Max Problems and Beyond

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Stochastic gradient descent (SGD) and randomized coordinate descent (RCD) are two of the workhorses for training modern automated decision systems. Intriguingly, convergence properties of these methods are not well-established as we move away from the spec ...

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Distributed Learning in Non-Convex Environments-Part I: Agreement at a Linear Rate

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Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments. Most available wor ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Large Steps in Inverse Rendering of Geometry

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Inverse reconstruction from images is a central problem in many scientific and engineering disciplines. Recent progress on differentiable rendering has led to methods that can efficiently differentiate the full process of image formation with respect to mi ...

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