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The goal of this paper is to debunk and dispel the magic behind black-box optimizers and stochastic optimizers. It aims to build a solid foundation on how and why the techniques work. This manuscript crystallizes this knowledge by deriving…

机器学习 · 计算机科学 2024-01-15 Jun Lu

An ensemble method is introduced that utilizes randomization and loss function gradients to compute a prediction. Multiple weakly-correlated estimators approximate the gradient at randomly sampled points on the error surface and are…

机器学习 · 计算机科学 2020-09-15 Nicholas Smith

We explore why many recently proposed robust estimation problems are efficiently solvable, even though the underlying optimization problems are non-convex. We study the loss landscape of these robust estimation problems, and identify the…

机器学习 · 统计学 2020-05-29 Banghua Zhu , Jiantao Jiao , Jacob Steinhardt

We show that the Wang-Landau algorithm can be formulated as a stochastic gradient descent algorithm minimizing a smooth and convex objective function, of which the gradient is estimated using Markov chain Monte Carlo iterations. The…

统计计算 · 统计学 2020-03-11 Chenguang Dai , Jun S. Liu

Accurate 6D object pose estimation is fundamental to robotic manipulation and grasping. Previous methods follow a local optimization approach which minimizes the distance between closest point pairs to handle the rotation ambiguity of…

计算机视觉与模式识别 · 计算机科学 2020-03-10 Meng Tian , Liang Pan , Marcelo H Ang , Gim Hee Lee

This work provides the first convergence analysis for the Randomized Block Coordinate Descent method for minimizing a function that is both H\"older smooth and block H\"older smooth. Our analysis applies to objective functions that are…

最优化与控制 · 数学 2024-03-14 Leandro Farias Maia , David Huckleberry Gutman

This paper extends algorithms that remove the fixed point bias of decentralized gradient descent to solve the more general problem of distributed optimization over subspace constraints. Leveraging the integral quadratic constraint…

最优化与控制 · 数学 2022-10-31 Dennis J. Marquis , Dany Abou Jaoude , Mazen Farhood , Craig A. Woolsey

This paper investigates distributed zeroth-order optimization for smooth nonconvex problems, targeting the trade-off between convergence rate and sampling cost per zeroth-order gradient estimation in current algorithms that use either the…

最优化与控制 · 数学 2026-04-10 Huaiyi Mu , Yujie Tang , Jie Song , Zhongkui Li

Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…

机器学习 · 计算机科学 2015-02-10 Alina Ene , Huy L. Nguyen

Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…

机器学习 · 计算机科学 2015-03-19 Alexander Rakhlin , Ohad Shamir , Karthik Sridharan

Stochastic gradient descent method and its variants constitute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are…

机器学习 · 计算机科学 2024-03-14 S. Ilker Birbil , Ozgur Martin , Gonenc Onay , Figen Oztoprak

Due to the increase in data availability in urban and regional studies, various spatial panel models have emerged to model spatial panel data, which exhibit spatial patterns and spatial dependencies between observations across time.…

统计方法学 · 统计学 2026-03-17 Michael Balzer , Adhen Benlahlou

The traditional way of estimating the gravitational field from observed motions of test objects is based on the virial relation between their kinetic and potential energy. We find a more efficient method. It is based on the natural…

天体物理学 · 物理学 2009-11-10 Andrei M. Beloborodov , Yuri levin

Minimizing the empirical risk is a popular training strategy, but for learning tasks where the data may be noisy or heavy-tailed, one may require many observations in order to generalize well. To achieve better performance under less…

机器学习 · 统计学 2018-10-16 Matthew J. Holland , Kazushi Ikeda

Anisotropic rotation averaging has recently been explored as a natural extension of respective isotropic methods. In the anisotropic formulation, uncertainties of the estimated relative rotations -- obtained via standard two-view…

计算机视觉与模式识别 · 计算机科学 2025-09-09 Yaroslava Lochman , Carl Olsson , Christopher Zach

Gradient descent and its variants are widely used in machine learning. However, oracle access of gradient may not be available in many applications, limiting the direct use of gradient descent. This paper proposes a method of estimating…

最优化与控制 · 数学 2019-10-07 Qinbo Bai , Mridul Agarwal , Vaneet Aggarwal

This paper introduces a differentiable representation for the optimization of boustrophedon path plans in convex polygons, explores an additional parameter of these path plans that can be optimized, discusses the properties of this…

机器人学 · 计算机科学 2024-02-21 Thomas Manzini , Robin Murphy

There introduce Particle Optimized Gradient Descent (POGD), an algorithm based on the gradient descent but integrates the particle swarm optimization (PSO) principle to achieve the iteration. From the experiments, this algorithm has…

机器学习 · 计算机科学 2022-10-20 Feihu Han , Sida Xing , Sui Yang Khoo

Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…

数据结构与算法 · 计算机科学 2019-02-19 Dmitrii Avdiukhin , Sergey Pupyrev , Grigory Yaroslavtsev

Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…

机器学习 · 统计学 2021-03-08 Nicole Mücke