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We introduce a generic scheme for accelerating first-order optimization methods in the sense of Nesterov, which builds upon a new analysis of the accelerated proximal point algorithm. Our approach consists of minimizing a convex objective…

Optimization and Control · Mathematics 2015-10-27 Hongzhou Lin , Julien Mairal , Zaid Harchaoui

We develop a distributed algorithm for convex Empirical Risk Minimization, the problem of minimizing large but finite sum of convex functions over networks. The proposed algorithm is derived from directly discretizing the second-order…

Optimization and Control · Mathematics 2018-11-07 Jingzhao Zhang , César A. Uribe , Aryan Mokhtari , Ali Jadbabaie

A framework is developed for applying accelerated methods to general hyperbolic programming, including linear, second-order cone, and semidefinite programming as special cases. The approach replaces a hyperbolic program with a convex…

Optimization and Control · Mathematics 2017-05-30 James Renegar

The optimization step in many machine learning problems rarely relies on vanilla gradient descent but it is common practice to use momentum-based accelerated methods. Despite these algorithms being widely applied to arbitrary loss…

Disordered Systems and Neural Networks · Physics 2021-10-29 Stefano Sarao Mannelli , Pierfrancesco Urbani

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…

Machine Learning · Statistics 2015-04-08 Nicolas Flammarion , Francis Bach

A set of accelerated first order algorithms with memory are proposed for minimising strongly convex functions. The algorithms are differentiated by their use of the iterate history for the gradient step. The increased convergence rate of…

Optimization and Control · Mathematics 2018-08-31 Ross Drummond , Stephen Duncan

The success of deep learning over the past decade mainly relies on gradient-based optimisation and backpropagation. This paper focuses on analysing the performance of first-order gradient-based optimisation algorithms, gradient descent and…

Optimization and Control · Mathematics 2022-12-08 Behnam Mafakheri , Iman Shames , Jonathan H. Manton

Accurate hardware performance models are critical to efficient code generation. They can be used by compilers to make heuristic decisions, by superoptimizers as a minimization objective, or by autotuners to find an optimal configuration for…

Convergence analysis of accelerated first-order methods for convex optimization problems are presented from the point of view of ordinary differential equation solvers. A new dynamical system, called Nesterov accelerated gradient flow, has…

Optimization and Control · Mathematics 2022-03-01 Hao Luo , Long Chen

Heavy Ball (HB) nowadays is one of the most popular momentum methods in non-convex optimization. It has been widely observed that incorporating the Heavy Ball dynamic in gradient-based methods accelerates the training process of modern…

Optimization and Control · Mathematics 2023-08-30 Jun-Kun Wang , Chi-Heng Lin , Andre Wibisono , Bin Hu

Policy gradient methods are widely used in reinforcement learning algorithms to search for better policies in the parameterized policy space. They do gradient search in the policy space and are known to converge very slowly. Nesterov…

Machine Learning · Computer Science 2018-04-26 K. Lakshmanan

Differentially private (stochastic) gradient descent is the workhorse of DP private machine learning in both the convex and non-convex settings. Without privacy constraints, second-order methods, like Newton's method, converge faster than…

Machine Learning · Computer Science 2023-05-23 Arun Ganesh , Mahdi Haghifam , Thomas Steinke , Abhradeep Thakurta

In this paper, we propose a unified two-phase scheme to accelerate any high-order regularized tensor approximation approach on the smooth part of a composite convex optimization model. The proposed scheme has the advantage of not needing to…

Optimization and Control · Mathematics 2020-07-06 Bo Jiang , Tianyi Lin , Shuzhong Zhang

This paper delves into the investigation of a distributed aggregative optimization problem within a network. In this scenario, each agent possesses its own local cost function, which relies not only on the local state variable but also on…

Optimization and Control · Mathematics 2025-04-01 Jiaxu Liu , Song Chen , Shengze Cai , Chao Xu , Jian Chu

We show that Nesterov acceleration is an optimal-order iterative regularization method for linear ill-posed problems provided that a parameter is chosen accordingly to the smoothness of the solution. This result is proven both for an a…

Numerical Analysis · Mathematics 2021-07-07 Stefan Kindermann

We provide improved convergence rates for various \emph{non-smooth} optimization problems via higher-order accelerated methods. In the case of $\ell_\infty$ regression, we achieves an $O(\epsilon^{-4/5})$ iteration complexity, breaking the…

Optimization and Control · Mathematics 2019-06-05 Brian Bullins , Richard Peng

In convex optimization, there is an {\em acceleration} phenomenon in which we can boost the convergence rate of certain gradient-based algorithms. We can observe this phenomenon in Nesterov's accelerated gradient descent, accelerated mirror…

Optimization and Control · Mathematics 2015-09-14 Andre Wibisono , Ashia C. Wilson

In this short note, we provide a simple version of an accelerated forward-backward method (a.k.a. Nesterov's accelerated proximal gradient method) possibly relying on approximate proximal operators and allowing to exploit strong convexity…

Optimization and Control · Mathematics 2022-01-24 Mathieu Barré , Adrien Taylor , Francis Bach

We study first-order optimization methods obtained by discretizing ordinary differential equations (ODEs) corresponding to Nesterov's accelerated gradient methods (NAGs) and Polyak's heavy-ball method. We consider three discretization…

Optimization and Control · Mathematics 2019-11-05 Bin Shi , Simon S. Du , Weijie J. Su , Michael I. Jordan

We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…

Optimization and Control · Mathematics 2025-05-02 Michael Muehlebach , Michael I. Jordan