  Online learning to rank is a sequential decision-making problem where in each
round the learning agent chooses a list of items and receives feedback in the
form of clicks from the user. Many sample-efficient algorithms have been
proposed for this problem that assume a specific click model connecting
rankings and user behavior. We propose a generalized click model that
encompasses many existing models, including the position-based and cascade
models. Our generalization motivates a novel online learning algorithm based on
topological sort, which we call TopRank. TopRank is (a) more natural than
existing algorithms, (b) has stronger regret guarantees than existing
algorithms with comparable generality, (c) has a more insightful proof that
leaves the door open to many generalizations, (d) outperforms existing
algorithms empirically.
