  We obtain sharp oracle inequalities for the empirical risk minimization
procedure in the regression model under the assumption that the target Y and
the model F are subgaussian. The bound we obtain is sharp in the minimax sense
if F is convex. Moreover, under mild assumptions on F, the error rate of ERM
remains optimal even if the procedure is allowed to perform with constant
probability. A part of our analysis is a new proof of minimax results for the
gaussian regression model.
