Learning without Concentration
  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. 
Shahar Mendelson
cs.LG stat.ML