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

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 no degradation in generalization ability as document lists become longer. We also provide novel generalization error bounds under ℓ1 regularization and faster convergence rates if the loss function is smooth.