Conference proceeding
A Simple Analysis for Exp-concave Empirical Minimization with Arbitrary Convex Regularizer
Proceedings of Machine Learning Research, Vol.84, pp.445-453
International Conference on Artificial Intelligence and Statistics (AISTATS) , 21st (Lanzarote, Spain, 2018)
04/2018
Abstract
In this paper, we present a simple analysis of {\bf fast rates} with {\it
high probability} of {\bf empirical minimization} for {\it stochastic composite
optimization} over a finite-dimensional bounded convex set with exponential
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 {\it high probability} for exponential
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 exponential concave empirical risk
minimization with and without {\it any} convex regularization. Our proof is
very simple only exploiting the covering number of a finite-dimensional bounded
set and a concentration inequality of random vectors.
Details
- Title: Subtitle
- A Simple Analysis for Exp-concave Empirical Minimization with Arbitrary Convex Regularizer
- Creators
- Tianbao YangZhe LiLijun Zhang
- Resource Type
- Conference proceeding
- Publication Details
- Proceedings of Machine Learning Research, Vol.84, pp.445-453
- Conference
- International Conference on Artificial Intelligence and Statistics (AISTATS) , 21st (Lanzarote, Spain, 2018)
- Language
- English
- Date published
- 04/2018
- Academic Unit
- Computer Science
- Record Identifier
- 9984259406402771
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