English
Related papers

Related papers: Randomized Greedy Algorithms for Neural Network Op…

200 papers

Greedy algorithms are widely used for problems in machine learning such as feature selection and set function optimization. Unfortunately, for large datasets, the running time of even greedy algorithms can be quite high. This is because for…

Machine Learning · Statistics 2017-03-09 Rajiv Khanna , Ethan Elenberg , Alexandros G. Dimakis , Sahand Negahban , Joydeep Ghosh

We consider a class of popular distributed non-convex optimization problems, in which agents connected by a network $\mathcal{G}$ collectively optimize a sum of smooth (possibly non-convex) local objective functions. We address the…

Optimization and Control · Mathematics 2020-01-08 Haoran Sun , Mingyi Hong

We propose a new gradient descent algorithm with added stochastic terms for finding the global optimizers of nonconvex optimization problems. A key component in the algorithm is the adaptive tuning of the randomness based on the value of…

Optimization and Control · Mathematics 2025-06-16 Björn Engquist , Kui Ren , Yunan Yang

We study the problem of distributed zero-order optimization for a class of strongly convex functions. They are formed by the average of local objectives, associated to different nodes in a prescribed network of connections. We propose a…

Optimization and Control · Mathematics 2021-06-29 Arya Akhavan , Massimiliano Pontil , Alexandre B. Tsybakov

Proximal gradient method has been playing an important role to solve many machine learning tasks, especially for the nonsmooth problems. However, in some machine learning problems such as the bandit model and the black-box learning problem,…

Optimization and Control · Mathematics 2019-02-19 Feihu Huang , Bin Gu , Zhouyuan Huo , Songcan Chen , Heng Huang

This paper addresses resource allocation problem with a separable objective function under a single linear constraint, formulated as maximizing $\sum_{j=1}^{n}R_j(x_j)$ subject to $\sum_{j=1}^{n}x_j=k$ and $x_j\in\{0,\dots,m\}$. While…

Data Structures and Algorithms · Computer Science 2025-09-10 Song Cao , Taikun Zhu , Kai Jin

We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. For this problem, lower bounds on the number of gradient computations and the number of communication…

Optimization and Control · Mathematics 2020-11-16 Dmitry Kovalev , Adil Salim , Peter Richtárik

``Composable core-sets'' are an efficient framework for solving optimization problems in massive data models. In this work, we consider efficient construction of composable core-sets for the determinant maximization problem. This can also…

Data Structures and Algorithms · Computer Science 2019-07-09 Piotr Indyk , Sepideh Mahabadi , Shayan Oveis Gharan , Alireza Rezaei

We show that Orthogonal Greedy Algorithms (Orthogonal Matching Pursuit) provides almost optimal approximation on the first [1/(20M)] steps for M-coherent dictionaries

Numerical Analysis · Mathematics 2010-03-30 Eugene Livshitz

We study the trade-offs between convergence rate and robustness to gradient errors in designing a first-order algorithm. We focus on gradient descent (GD) and accelerated gradient (AG) methods for minimizing strongly convex functions when…

Optimization and Control · Mathematics 2019-11-07 Necdet Serhat Aybat , Alireza Fallah , Mert Gurbuzbalaban , Asuman Ozdaglar

In this paper we introduce a class of novel distributed algorithms for solving stochastic big-data convex optimization problems over directed graphs. In the addressed set-up, the dimension of the decision variable can be extremely high and…

Optimization and Control · Mathematics 2020-10-06 Francesco Farina , Giuseppe Notarstefano

Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…

We study greedy-type algorithms such that at a greedy step we pick several dictionary elements contrary to a single dictionary element in standard greedy-type algorithms. We call such greedy algorithms {\it super greedy algorithms}. The…

Numerical Analysis · Mathematics 2010-10-27 Entao Liu , Vladimir N. Temlyakov

The design of good heuristics or approximation algorithms for NP-hard combinatorial optimization problems often requires significant specialized knowledge and trial-and-error. Can we automate this challenging, tedious process, and learn the…

Machine Learning · Computer Science 2018-02-23 Hanjun Dai , Elias B. Khalil , Yuyu Zhang , Bistra Dilkina , Le Song

We consider distributed optimization where the objective function is spread among different devices, each sending incremental model updates to a central server. To alleviate the communication bottleneck, recent work proposed various schemes…

Optimization and Control · Mathematics 2019-04-11 Samuel Horváth , Dmitry Kovalev , Konstantin Mishchenko , Sebastian Stich , Peter Richtárik

We consider unconstrained randomized optimization of convex objective functions. We analyze the Random Pursuit algorithm, which iteratively computes an approximate solution to the optimization problem by repeated optimization over a…

Optimization and Control · Mathematics 2012-05-25 Sebastian U. Stich , Christian L. Müller , Bernd Gärtner

In this paper we develop a procedure to deal with a family of parameter-dependent ill-posed problems, for which the exact solution in general does not exist. The original problems are relaxed by considering corresponding approximate ones,…

Analysis of PDEs · Mathematics 2022-06-29 Martin Lazar , Enrique Zuazua

We introduce biased gradient oracles to capture a setting where the function measurements have an estimation error that can be controlled through a batch size parameter. Our proposed oracles are appealing in several practical contexts, for…

Machine Learning · Computer Science 2021-05-18 Nirav Bhavsar , Prashanth L. A

The approximation of a discrete probability distribution $\mathbf{t}$ by an $M$-type distribution $\mathbf{p}$ is considered. The approximation error is measured by the informational divergence $\mathbb{D}(\mathbf{t}\Vert\mathbf{p})$, which…

Information Theory · Computer Science 2016-07-28 Bernhard C. Geiger , Georg Böcherer

In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only…

Optimization and Control · Mathematics 2011-01-19 Raymond Hemmecke , Shmuel Onn , Robert Weismantel