  We consider the generalization ability of algorithms for learning to rank at
a query level, a problem also called subset ranking. Existing generalization
error bounds necessarily degrade as the size of the document list associated
with a query increases. We show that such a degradation is not intrinsic to the
problem. For several loss functions, including the cross-entropy loss used in
the well known ListNet method, there is \emph{no} degradation in generalization
ability as document lists become longer. We also provide novel generalization
error bounds under $\ell_1$ regularization and faster convergence rates if the
loss function is smooth.
