Coordinate Descent Face-Off: Primal or Dual?

Dominik Csiba, Peter Richtárik

Research output: Contribution to conferencePaperpeer-review

Abstract

Randomized coordinate descent (RCD) methods are state-of-the-art algorithms for training linear predictors via minimizing regularized empirical risk. When the number of examples ($n$) is much larger than the number of features ($d$), a common strategy is to apply RCD to the dual problem. On the other hand, when the number of features is much larger than the number of examples, it makes sense to apply RCD directly to the primal problem. In this paper we provide the first joint study of these two approaches when applied to L2-regularized ERM. First, we show through a rigorous analysis that for dense data, the above intuition is precisely correct. However, we find that for sparse and structured data, primal RCD can significantly outperform dual RCD even if $d \ll n$, and vice versa, dual RCD can be much faster than primal RCD even if $n \ll d$. Moreover, we show that, surprisingly, a single sampling strategy minimizes both the (bound on the) number of iterations and the overall expected complexity of RCD. Note that the latter complexity measure also takes into account the average cost of the iterations, which depends on the structure and sparsity of the data, and on the sampling strategy employed. We confirm our theoretical predictions using extensive experiments with both synthetic and real data sets.
Original languageEnglish
Number of pages22
Publication statusPublished - 7 Apr 2018
Event29th international conference on algorithmetic learning - Lanzarote, Spain
Duration: 7 Apr 20189 Apr 2018
http://www.cs.cornell.edu/conferences/alt2018/

Conference

Conference29th international conference on algorithmetic learning
CountrySpain
Period7/04/189/04/18
Internet address

Keywords

  • math.OC

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