大规模最小二乘问题的约束随机梯度下降

Yang Mu, W. Ding, Tianyi Zhou, D. Tao
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引用次数: 6

摘要

最小二乘问题是统计学、机器学习和数据挖掘中最重要的回归问题之一。本文提出了求解大规模最小二乘问题的约束随机梯度下降(CSGD)算法。CSGD通过施加线性回归线经过所有数据点的平均值的可证明约束来改进随机梯度下降(SGD)。该方法得到了最佳后悔界$O(\log{T})$,并且收敛速度是所有一阶方法中最快的。实证研究通过将CSGD与SGD和其他最先进的方法进行比较,证明了CSGD的有效性。通过实例说明了如何使用CSGD优化基于最小二乘问题的SGD,以获得更好的性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Constrained stochastic gradient descent for large-scale least squares problem
The least squares problem is one of the most important regression problems in statistics, machine learning and data mining. In this paper, we present the Constrained Stochastic Gradient Descent (CSGD) algorithm to solve the large-scale least squares problem. CSGD improves the Stochastic Gradient Descent (SGD) by imposing a provable constraint that the linear regression line passes through the mean point of all the data points. It results in the best regret bound $O(\log{T})$, and fastest convergence speed among all first order approaches. Empirical studies justify the effectiveness of CSGD by comparing it with SGD and other state-of-the-art approaches. An example is also given to show how to use CSGD to optimize SGD based least squares problems to achieve a better performance.
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