Related papers: Global convergence of gradient descent for phase r…

Approximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute…

Global minimization is a fundamental challenge in optimization, especially in machine learning, where finding the global minimum of a function directly impacts model performance and convergence. This article introduces a novel optimization…

Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. Due to the highly nonconvex nature of the empirical loss, state-of-the-art procedures often…

Gradient descent is the primary workhorse for optimizing large-scale problems in machine learning. However, its performance is highly sensitive to the choice of the learning rate. A key limitation of gradient descent is its lack of natural…

In our work, we propose a novel yet simple approach to obtain an adaptive learning rate for gradient-based descent methods on classification tasks. Instead of the traditional approach of selecting adaptive learning rates via the decayed…

We give a derivation of the method of conjugate gradients based on the requirement that each iterate minimizes a strictly convex quadratic on the space spanned by the previously observed gradients. Rather than verifying that the search…

Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent…

We analyze the global convergence of gradient descent for deep linear residual networks by proposing a new initialization: zero-asymmetric (ZAS) initialization. It is motivated by avoiding stable manifolds of saddle points. We prove that…

In this paper, we aim to reconstruct an n-dimensional real vector from m phaseless measurements corrupted by an additive noise. We extend the noiseless framework developed in [15], based on mirror descent (or Bregman gradient descent), to…

This paper deals with local criteria for the convergence to a global minimiser for gradient flow trajectories and their discretisations. To obtain quantitative estimates on the speed of convergence, we consider variations on the classical…

We consider gradient descent with constant stepsizes and derive exact worst-case convergence rates on the minimum gradient norm of the iterates. Our analysis covers all possible stepsizes and arbitrary upper/lower bounds on the curvature of…

We give curvature-dependant convergence rates for the optimization of weakly convex functions defined on a manifold of 1-bounded geometry via Riemannian gradient descent and via the dynamic trivialization algorithm. In order to do this, we…

In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…

We analyze the convergence of a nonlocal gradient descent method for minimizing a class of high-dimensional non-convex functions, where a directional Gaussian smoothing (DGS) is proposed to define the nonlocal gradient (also referred to as…

Gradient clipping is a popular modification to standard (stochastic) gradient descent, at every iteration limiting the gradient norm to a certain value $c >0$. It is widely used for example for stabilizing the training of deep learning…

Due to the multi-linearity of tensors, most algorithms for tensor optimization problems are designed based on the block coordinate descent method. Such algorithms are widely employed by practitioners for their implementability and…

Gradient descent, when applied to the task of logistic regression, outputs iterates which are biased to follow a unique ray defined by the data. The direction of this ray is the maximum margin predictor of a maximal linearly separable…

Gradient descent is a simple and widely used optimization method for machine learning. For homogeneous linear classifiers applied to separable data, gradient descent has been shown to converge to the maximal margin (or equivalently, the…

Stochastic gradient descent (SGD) gives an optimal convergence rate when minimizing convex stochastic objectives $f(x)$. However, in terms of making the gradients small, the original SGD does not give an optimal rate, even when $f(x)$ is…

We review convergence and behavior of stochastic gradient descent for convex and nonconvex optimization, establishing various conditions for convergence to zero of the variance of the gradient of the objective function, and presenting a…