Volume 16, Number 3
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
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.
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