  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.
