Distributed learning with regularized least squares

Shao Bo Lin, Xin Guo, Ding Xuan Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

53 Citations (Scopus)

Abstract

We study distributed learning with the least squares regularization scheme in a reproducing kernel Hilbert space (RKHS). By a divide-and-conquer approach, the algorithm partitions a data set into disjoint data subsets, applies the least squares regularization scheme to each data subset to produce an output function, and then takes an average of the individual output functions as a final global estimator or predictor. We show with error bounds and learning rates in expectation in both the L2-metric and RKHS-metric that the global output function of this distributed learning is a good approximation to the algorithm processing the whole data in one single machine. Our derived learning rates in expectation are optimal and stated in a general setting without any eigenfunction assumption. The analysis is achieved by a novel second order decomposition of operator differences in our integral operator approach. Even for the classical least squares regularization scheme in the RKHS associated with a general kernel, we give the best learning rate in expectation in the literature.
Original languageEnglish
Pages (from-to)1-31
Number of pages31
JournalJournal of Machine Learning Research
Volume18
Publication statusPublished - 1 Sep 2017

Keywords

  • Distributed learning
  • Divide-and-conquer
  • Error analysis
  • Integral operator second order decomposition

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence

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