  In binary classification and regression problems, it is well understood that
Lipschitz continuity and smoothness of the loss function play key roles in
governing generalization error bounds for empirical risk minimization
algorithms. In this paper, we show how these two properties affect
generalization error bounds in the learning to rank problem. The learning to
rank problem involves vector valued predictions and therefore the choice of the
norm with respect to which Lipschitz continuity and smoothness are defined
becomes crucial. Choosing the $\ell_\infty$ norm in our definition of Lipschitz
continuity allows us to improve existing bounds. Furthermore, under smoothness
assumptions, our choice enables us to prove rates that interpolate between
$1/\sqrt{n}$ and $1/n$ rates. Application of our results to ListNet, a popular
learning to rank method, gives state-of-the-art performance guarantees.
