Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

Matrix regularization techniques for online multitask learning

Alekh Agarwal, Alexander Rakhlin and Peter Bartlett

EECS Department
University of California, Berkeley
Technical Report No. UCB/EECS-2008-138
October 23, 2008

http://www.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-138.pdf

In this paper we examine the problem of prediction with expert advice in a setup where the learner is presented with a sequence of examples coming from different tasks. In order for the learner to be able to benefit from performing multiple tasks simultaneously, we make assumptions of task relatedness by constraining the comparator to use a lesser number of best experts than the number of tasks. We show how this corresponds naturally to learning under spectral or structural matrix constraints, and propose regularization techniques to enforce the constraints. The regularization techniques proposed here are interesting in their own right and multitask learning is just one application for the ideas. A theoretical analysis of one such regularizer is performed, and a regret bound that shows benefits of this setup is reported.


BibTeX citation:

@techreport{Agarwal:EECS-2008-138,
    Author = {Agarwal, Alekh and Rakhlin, Alexander and Bartlett, Peter},
    Title = {Matrix regularization techniques for online multitask learning},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {2008},
    Month = {Oct},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-138.html},
    Number = {UCB/EECS-2008-138},
    Abstract = {In this paper we examine the problem of prediction with expert advice in a setup where the learner is presented with a sequence of examples coming from different tasks. In order for the learner to be able to benefit from performing multiple tasks simultaneously, we make assumptions of task
relatedness by constraining the comparator to use a lesser number of <i>best</i> experts than the number of tasks. We show how this corresponds naturally to learning under spectral or structural matrix constraints, and propose regularization techniques to enforce the constraints. The regularization techniques proposed here are interesting in their own right and multitask learning is just one application for the ideas. A theoretical analysis of one such regularizer is performed, and a regret bound that shows benefits of this setup is reported.}
}

EndNote citation:

%0 Report
%A Agarwal, Alekh
%A Rakhlin, Alexander
%A Bartlett, Peter
%T Matrix regularization techniques for online multitask learning
%I EECS Department, University of California, Berkeley
%D 2008
%8 October 23
%@ UCB/EECS-2008-138
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-138.html
%F Agarwal:EECS-2008-138