Generalization error bounds for learning to rank: Does the length of document lists matter?

Abstract: 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.