arXiv research

Accelerates coordinate descent methods for machine learning problems.

This work accelerates gradient descent with anytime convergence guarantees.

AGNES accelerates gradient descent with noisy gradients.

HF-opt uses Hamiltonian dynamics to optimize functions, achieving accelerated rates with randomized integration time.

Stochastic gradient descent on manifolds improves low-rank approximation.

We study learning properties of accelerated gradient descent methods for linear least-squares in Hilbert spaces. We analyze the implicit regularization properties of Nesterov acceleration and a variant of heavy-ball in terms of corresponding learning error bounds. Our results show that acceleration can provides faster …

There is widespread sentiment that it is not possible to effectively utilize fast gradient methods (e.g. Nesterov's acceleration, conjugate gradient, heavy ball) for the purposes of stochastic optimization due to their instability and error accumulation, a notion made precise in d'Aspremont 2008 and Devolder, Glineur, …

Continuized Nesterov acceleration accelerates stochastic gradient descent and gossip algorithms.

In this work we introduce a conditional accelerated lazy stochastic gradient descent algorithm with optimal number of calls to a stochastic first-order oracle and convergence rate $O\left(\frac{1}{\varepsilon^2}\right)$ improving over the projection-free, Online Frank-Wolfe based stochastic gradient descent of Hazan an…

Stochastic gradient descent (\textsc{Sgd}) methods are the most powerful optimization tools in training machine learning and deep learning models. Moreover, acceleration (a.k.a. momentum) methods and diagonal scaling (a.k.a. adaptive gradient) methods are the two main techniques to improve the slow convergence of \text…

FedAc accelerates Federated Averaging for distributed optimization.

Accelerates Riemannian gradient methods with extrapolation.

Accelerated gradient method's stability deteriorates exponentially with steps.

Accelerates MMLE using SVGD with Nesterov acceleration.

Chebyshev steps improve convergence in deep-unfolded gradient descent.

We present a unifying framework for adapting the update direction in gradient-based iterative optimization methods. As natural special cases we re-derive classical momentum and Nesterov's accelerated gradient method, lending a new intuitive interpretation to the latter algorithm. We show that a new algorithm, which we …

Stacking improves deep neural network training efficiency.

Large stepsizes can accelerate gradient descent for logistic regression.

Accelerated optimization methods improve robustness and privacy in estimation.

New methods accelerate gradient descent for convex and strongly convex functions.

Accelerates ERM problems with LPI-GD and improved oracle complexity.

New algorithms accelerate SVGD convergence using deep unfolding.

We propose accelerated randomized coordinate descent algorithms for stochastic optimization and online learning. Our algorithms have significantly less per-iteration complexity than the known accelerated gradient algorithms. The proposed algorithms for online learning have better regret performance than the known rando…

Deep unfolding accelerates MCMC-based COP solvers.

We consider gradient descent with `momentum', a widely used method for loss function minimization in machine learning. This method is often used with `Nesterov acceleration', meaning that the gradient is evaluated not at the current position in parameter space, but at the estimated position after one step. In this work…

ASVGD accelerates SVGD for efficient sampling.

Fractal learning rate schedules accelerate vanilla gradient descent.

We present theoretical results on the convergence of \emph{non-convex} accelerated gradient descent in matrix factorization models with $\ell_2$-norm loss. The purpose of this work is to study the effects of acceleration in non-convex settings, where provable convergence with acceleration should not be considered a \em…

Accelerated method finds critical points faster on manifolds.

Federated learning (FL) provides a communication-efficient approach to solve machine learning problems concerning distributed data, without sending raw data to a central server. However, existing works on FL only utilize first-order gradient descent (GD) and do not consider the preceding iterations to gradient update w…

A new accelerated method with simpler momentum update rules.

We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike SVRG, our method can be directly applied to non-strongly and strongly convex prob…

This paper analyzes and guarantees convergence of prior-guided ZO algorithms.

Two new algorithms improve neural architecture search efficiency.

We show that accelerated gradient descent, averaged gradient descent and the heavy-ball method for non-strongly-convex problems may be reformulated as constant parameter second-order difference equation algorithms, where stability of the system is equivalent to convergence at rate O(1/n 2), where n is the number of ite…

Nesterov's accelerated gradient descent (AGD), an instance of the general family of "momentum methods", provably achieves faster convergence rate than gradient descent (GD) in the convex setting. However, whether these methods are superior to GD in the nonconvex setting remains open. This paper studies a simple variant…

SpecGD mitigates misalignment in phase retrieval models with anisotropic inputs.

Momentum based stochastic gradient methods such as heavy ball (HB) and Nesterov's accelerated gradient descent (NAG) method are widely used in practice for training deep networks and other supervised learning models, as they often provide significant improvements over stochastic gradient descent (SGD). Rigorously speak…

Information that is stored in an encrypted format is, by definition, usually not amenable to statistical analysis or machine learning methods. In this paper we present detailed analysis of coordinate and accelerated gradient descent algorithms which are capable of fitting least squares and penalised ridge regression mo…

Accelerated coordinate descent is widely used in optimization due to its cheap per-iteration cost and scalability to large-scale problems. Up to a primal-dual transformation, it is also the same as accelerated stochastic gradient descent that is one of the central methods used in machine learning. In this paper, we imp…

Polyak's momentum accelerates training of neural networks.

Preconditioned non-convex gradient descent improves noisy matrix estimation.

Improved SGD for non-strongly-convex regression with faster convergence.

Gradient tree boosting is a prediction algorithm that sequentially produces a model in the form of linear combinations of decision trees, by solving an infinite-dimensional optimization problem. We combine gradient boosting and Nesterov's accelerated descent to design a new algorithm, which we call AGB (for Accelerated…

A fast method for training linear classifiers maximizes margins.

Large stepsize GD for logistic regression converges faster than expected.

ScaledGD accelerates ill-conditioned low-rank estimation.

We introduce a generic scheme for accelerating gradient-based optimization methods in the sense of Nesterov. The approach, called Catalyst, builds upon the inexact accelerated proximal point algorithm for minimizing a convex objective function, and consists of approximately solving a sequence of well-chosen auxiliary p…