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Online learning to rank is a core problem in information retrieval andmachine learning. Many provably efficient algorithms have been recentlyproposed for this problem in specific click models. The click model is a modelof how the user interacts with a list of documents. Though these results aresignificant, their impact on practice is limited, because all proposedalgorithms are designed for specific click models and lack convergenceguarantees in other models. In this work, we propose BatchRank, the firstonline learning to rank algorithm for a broad class of click models. The classencompasses two most fundamental click models, the cascade and position-basedmodels. We derive a gap-dependent upper bound on the $T$-step regret ofBatchRank and evaluate it on a range of web search queries. We observe thatBatchRank outperforms ranked bandits and is more robust than CascadeKL-UCB, anexisting algorithm for the cascade model.

Online Learning to Rank in Stochastic Click Models