A Simple Analysis for Exp-concave Empirical Minimization with Arbitrary Convex Regularizer

نویسندگان

  • Tianbao Yang
  • Zhe Li
  • Lijun Zhang
چکیده

In this paper, we present a simple analysis of fast rates with high probability of empirical minimization for stochastic composite optimization over a finite-dimensional bounded convex set with exponentially concave loss functions and an arbitrary convex regularization. To the best of our knowledge, this result is the first of its kind. As a byproduct, we can directly obtain the fast rate with high probability for exponentially concave empirical risk minimization with and without any convex regularization, which not only extends existing results of empirical risk minimization but also provides a unified framework for analyzing exponentially concave empirical risk minimization with and without any convex regularization. Our proof is very simple only exploiting the covering number of a finitedimensional bounded set and a concentration inequality of random vectors.

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عنوان ژورنال:
  • CoRR

دوره abs/1709.02909  شماره 

صفحات  -

تاریخ انتشار 2017