  We obtain sharp bounds on the performance of Empirical Risk Minimization
performed in a convex class and with respect to the squared loss, without
assuming that class members and the target are bounded functions or have
rapidly decaying tails.
  Rather than resorting to a concentration-based argument, the method used here
relies on a `small-ball' assumption and thus holds for classes consisting of
heavy-tailed functions and for heavy-tailed targets.
  The resulting estimates scale correctly with the `noise level' of the
problem, and when applied to the classical, bounded scenario, always improve
the known bounds.
