This video was recorded at 27th Annual Conference on Learning Theory (COLT), Barcelona 2014. We obtain sharp bounds on the convergence rate of Empirical Risk Minimization performed in a convex class and with respect to the squared loss, without any boundedness assumptions on class members or on the target. Rather than resorting to a concentration-based argument, the method relies on a 'small-ball' assumption and thus holds for heavy-tailed sampling and heavy-tailed targets. Moreover, the resulting estimates scale correctly with the 'noise level' of the problem. When applied to the classical, bounded scenario, the method always improves the known estimates.
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