Perceptron-like Algorithms and Generalization Bounds for Learning to Rank

TL;DR

This paper introduces perceptron-like algorithms for online learning to rank and establishes generalization bounds for batch learning with convex surrogates, supported by novel listwise large margin ranking surrogates.

Contribution

It presents a perceptron-like online ranking algorithm, a new family of listwise large margin surrogates, and a generalization bound independent of the number of objects per query.

Findings

Perceptron-like online ranking algorithm with theoretical guarantees.

A new family of listwise large margin ranking surrogates.

Generalization bounds for batch learning with linear ranking functions.

Abstract

Learning to rank is a supervised learning problem where the output space is the space of rankings but the supervision space is the space of relevance scores. We make theoretical contributions to the learning to rank problem both in the online and batch settings. First, we propose a perceptron-like algorithm for learning a ranking function in an online setting. Our algorithm is an extension of the classic perceptron algorithm for the classification problem. Second, in the setting of batch learning, we introduce a sufficient condition for convex ranking surrogates to ensure a generalization bound that is independent of number of objects per query. Our bound holds when linear ranking functions are used: a common practice in many learning to rank algorithms. En route to developing the online algorithm and generalization bound, we propose a novel family of listwise large margin ranking surrogates. Our novel surrogate family is obtained by modifying a well-known pairwise large margin ranking surrogate and is distinct from the listwise large margin surrogates developed using the structured prediction framework. Using the proposed family, we provide a guaranteed upper bound on the cumulative NDCG (or MAP) induced loss under the perceptron-like algorithm. We also show that the novel surrogates satisfy the generalization bound condition.