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arXiv 2008.10020cs.LGcs.SYeess.SPeess.SYstat.ML
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多核被动随机梯度算法与迁移学习

Multi-kernel Passive Stochastic Gradient Algorithms and Transfer Learning

Cornell University(康奈尔大学);University of Connecticut(康涅狄格大学)

Vikram Krishnamurthy, George Yin

摘要:

本文提出了一种新的被动随机梯度算法。在被动随机近似中,随机梯度算法对评估成本函数的噪声梯度的位置没有控制。经典的被动随机梯度算法使用近似Dirac delta的核来基于它们离期望点的距离来对梯度进行加权。本文构造了一种多核被动随机梯度算法。该算法在高维问题中表现得更好,并结合方差减少。分析了多核算法的弱收敛性和收敛速度。在数值例子中,我们研究了多核版本的被动最小均方(LMS)算法的迁移学习的性能与经典的被动版本进行比较。

英文摘要:

This paper develops a novel passive stochastic gradient algorithm. In passive stochastic approximation, the stochastic gradient algorithm does not have control over the location where noisy gradients of the cost function are evaluated. Classical passive stochastic gradient algorithms use a kernel that approximates a Dirac delta to weigh the gradients based on how far they are evaluated from the desired point. In this paper we construct a multi-kernel passive stochastic gradient algorithm. The algorithm performs substantially better in high dimensional problems and incorporates variance reduction. We analyze the weak convergence of the multi-kernel algorithm and its rate of convergence. In numerical examples, we study the multi-kernel version of the passive least mean squares (LMS) algorithm for transfer learning to compare the performance with the classical passive version.

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