  Let $\cF$ be a set of $M$ classification procedures with values in $[-1,1]$.
Given a loss function, we want to construct a procedure which mimics at the
best possible rate the best procedure in $\cF$. This fastest rate is called
optimal rate of aggregation. Considering a continuous scale of loss functions
with various types of convexity, we prove that optimal rates of aggregation can
be either $((\log M)/n)^{1/2}$ or $(\log M)/n$. We prove that, if all the $M$
classifiers are binary, the (penalized) Empirical Risk Minimization procedures
are suboptimal (even under the margin/low noise condition) when the loss
function is somewhat more than convex, whereas, in that case, aggregation
procedures with exponential weights achieve the optimal rate of aggregation.
