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

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