Generalization error bounds for learning to rank: Does the length of document lists matter?
This addresses a key theoretical issue in information retrieval for researchers and practitioners, providing insights that could improve ranking algorithms, though it appears incremental as it builds on existing bounds.
The paper tackles the problem of generalization error bounds in learning to rank, specifically whether longer document lists degrade performance, and shows that for certain loss functions like cross-entropy, there is no such degradation, with novel bounds under regularization and faster rates for smooth losses.
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.