Gradient Sliding Schemes for Large-scale Optimization and Data Analysis

用于大规模优化和数据分析的梯度滑动方案

基本信息

  • 批准号:
    1637474
  • 负责人:
  • 金额:
    $ 26.67万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2016
  • 资助国家:
    美国
  • 起止时间:
    2016-02-15 至 2019-10-31
  • 项目状态:
    已结题

项目摘要

The rapid advances in technology for digital data collection have led to significant increases in the size and complexity of data sets, sometimes known as big data. Optimization models, when combined with novel statistical analysis, have been proven fruitful in analyzing these complex datasets. However, optimization problems arising from these applications often involve nonsmooth components that can significantly slow down the convergence of existing optimization algorithms. Moreover, the complex datasets are so big and often distributed over different storage locations that the usual assumption that an entire dataset can be completely traversed in each iteration of the algorithm is unrealistic. Gradient sliding schemes do not require this assumption and hence are ideally suited for optimization with big data. The research aims at tackling these computational challenges through the design, analysis, and implementation of a novel class of optimization algorithms using gradient sliding schemes. The effectiveness of these new optimization algorithms will be demonstrated by solving problems in image processing and machine learning.The gradient sliding algorithms are first-order methods that use first-order information (gradients and function values) exclusively in addition to some auxiliary operations, such as projection over the feasible set. As opposed to existing first-order methods, gradient sliding methods can skip the computation of gradients from time to time, while still preserving the optimal convergence properties for solving different types of large-scale optimization problems. This research will also study a new class of conditional gradient sliding methods that require a linear optimization rather than a more involved projection over the feasible set in each iteration. These algorithms are expected to exhibit optimal rate of convergence in terms of both the number of gradient computations and the number of times for solving the linear optimization subproblem. Moreover, randomized variants of these gradient sliding algorithms which are amenable to parallel/distributed computing will also be studied. When applied to data analysis, these algorithms can reduce, by orders of magnitude, the number of traverses through the datasets, the computational cost associated with the involved matrix-vector multiplications, as well as the communication costs for the distributed datasets.
数字数据收集技术的迅速发展导致数据集(有时称为大数据)的规模和复杂性显著增加。优化模型,当结合新的统计分析,已被证明是卓有成效的分析这些复杂的数据集。然而,从这些应用程序中产生的优化问题往往涉及非光滑组件,可以显着减缓现有的优化算法的收敛。此外,复杂的数据集是如此之大,往往分布在不同的存储位置,通常的假设,整个数据集可以完全遍历在算法的每次迭代是不现实的。梯度滑动方案不需要这个假设,因此非常适合大数据优化。 该研究旨在通过设计,分析和实现一类新的优化算法,使用梯度滑动计划来解决这些计算挑战。 这些新的优化算法的有效性将通过解决图像处理和机器学习中的问题来证明。梯度滑动算法是一阶方法,除了一些辅助操作之外,还专门使用一阶信息(梯度和函数值),例如在可行集上的投影。与现有的一阶方法相反,梯度滑动方法可以不时地跳过梯度的计算,同时仍然保留用于解决不同类型的大规模优化问题的最佳收敛特性。本研究还将研究一类新的条件梯度滑动方法,该方法需要线性优化,而不是在每次迭代中在可行集上进行更复杂的投影。这些算法预计将表现出最佳的收敛速度的梯度计算的数量和解决线性优化子问题的次数。此外,这些梯度滑动算法,这是服从并行/分布式计算的随机变量也将进行研究。 当应用于数据分析时,这些算法可以按数量级减少遍历数据集的次数、与所涉及的矩阵向量乘法相关联的计算成本以及分布式数据集的通信成本。

项目成果

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Guanghui Lan其他文献

A simple uniformly optimal method without line search for convex optimization
一种简单的无线搜索凸优化一致最优方法
  • DOI:
    10.48550/arxiv.2310.10082
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Tianjiao Li;Guanghui Lan
  • 通讯作者:
    Guanghui Lan
Stochastic Approximation Methods and Their Finite-Time Convergence Properties
随机逼近方法及其有限时间收敛性质
  • DOI:
    10.1007/978-1-4939-1384-8_7
  • 发表时间:
    2015
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Saeed Ghadimi;Guanghui Lan
  • 通讯作者:
    Guanghui Lan
Policy Optimization over General State and Action Spaces
  • DOI:
    10.48550/arxiv.2211.16715
  • 发表时间:
    2022-11
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Guanghui Lan
  • 通讯作者:
    Guanghui Lan
Convex optimization under inexact first-order information
  • DOI:
  • 发表时间:
    2009-06
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Guanghui Lan
  • 通讯作者:
    Guanghui Lan
Deterministic Convex Optimization
确定性凸优化
  • DOI:
    10.1007/978-3-030-39568-1_3
  • 发表时间:
    2020
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Guanghui Lan
  • 通讯作者:
    Guanghui Lan

Guanghui Lan的其他文献

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{{ truncateString('Guanghui Lan', 18)}}的其他基金

Collaborative Research: Algorithms for Optimal Adaptive Enrichment Design in Randomized Trial
协作研究:随机试验中最佳自适应富集设计的算法
  • 批准号:
    1953199
  • 财政年份:
    2020
  • 资助金额:
    $ 26.67万
  • 项目类别:
    Standard Grant
CIF: Small: Collaborative Research: Acceleration Algorithms for Large-scale Nonconvex Optimization
CIF:小型:协作研究:大规模非凸优化的加速算法
  • 批准号:
    1909298
  • 财政年份:
    2019
  • 资助金额:
    $ 26.67万
  • 项目类别:
    Standard Grant
CAREER: Reduced-order Methods for Big-Data Challenges in Nonlinear and Stochastic Optimization
职业:非线性和随机优化中大数据挑战的降阶方法
  • 批准号:
    1637473
  • 财政年份:
    2016
  • 资助金额:
    $ 26.67万
  • 项目类别:
    Standard Grant
Gradient Sliding Schemes for Large-scale Optimization and Data Analysis
用于大规模优化和数据分析的梯度滑动方案
  • 批准号:
    1537414
  • 财政年份:
    2015
  • 资助金额:
    $ 26.67万
  • 项目类别:
    Standard Grant
CAREER: Reduced-order Methods for Big-Data Challenges in Nonlinear and Stochastic Optimization
职业:非线性和随机优化中大数据挑战的降阶方法
  • 批准号:
    1254446
  • 财政年份:
    2013
  • 资助金额:
    $ 26.67万
  • 项目类别:
    Standard Grant
Theory and Applications of Stochastic First-order Methods for Large-scale Stochastic Convex Optimization
大规模随机凸优化的随机一阶方法的理论与应用
  • 批准号:
    1000347
  • 财政年份:
    2010
  • 资助金额:
    $ 26.67万
  • 项目类别:
    Standard Grant

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职业:基于滑动铁电的非易失性存储器件
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    2339093
  • 财政年份:
    2024
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    2024
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职业:层状量子材料中滑动铁电性、自旋和电荷排序的相互作用
  • 批准号:
    2237761
  • 财政年份:
    2023
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通过向三指呈现滚动和滑动的触觉提示,实现元宇宙中灵巧的抓取操作
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  • 财政年份:
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  • 财政年份:
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Collaborative Research: Far-from-equilibrium surfaces of high entropy alloys: interplay between frictional sliding and corrosion damage
合作研究:高熵合金的非平衡表面:摩擦滑动与腐蚀损伤之间的相互作用
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