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Sharper lower bounds on the performance of the empirical risk minimization algorithm

Lecue, G; Mendelson, Shahar


We present an argument based on the multidimensional and the uniform central limit theorems, proving that, under some geometrical assumptions between the target function T and the learning class F, the excess risk of the empirical risk minimization algorithm is lower bounded by Esup q∈Q Gq/δ,/n where (Gq)q∈Q is a canonical Gaussian process associated with Q (a well chosen subset of F) and δ is a parameter governing the oscillations of the empirical excess risk function over a small ball in F.

CollectionsANU Research Publications
Date published: 2010
Type: Journal article
Source: Bernoulli
DOI: 10.3150/09-BEJ225


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