Lower Bounds for the Empirical Minimization Algorithm

In this correspondence, we present a simple argument that proves that under mild geometric assumptions on the class
F
and the set of target functions
T
, the empirical minimization algorithm cannot yield a uniform error rate that is faster than 1/radic
(k)
in the function learning setup. This result holds for various loss functionals and the target functions from
T
that cause the slow uniform error rate are clearly exhibited.