Paper detail

Exploiting Correlation to Achieve Faster Learning Rates in Low-Rank Preference Bandits

We introduce the \emph{Correlated Preference Bandits} problem with random utility-based choice models (RUMs), where the goal is to identify the best item from a given pool of $n$ items through online subsetwise preference feedback. We investigate whether models with a simple correlation structure, e.g. low rank, can result in faster learning rates. While we show that the problem can be impossible to solve for the general `low rank' choice models, faster learning rates can be attained assuming more structured item correlations. In particular, we introduce a new class of \emph{Block-Rank} based RUM model, where the best item is shown to be $(ε,δ)$-PAC learnable with only $O(r ε^{-2} \log(n/δ))$ samples. This improves on the standard sample complexity bound of $\tilde{O}(nε^{-2} \log(1/δ))$ known for the usual learning algorithms which might not exploit the item-correlations ($r \ll n$). We complement the above sample complexity with a matching lower bound (up to logarithmic factors), justifying the tightness of our analysis. Surprisingly, we also show a lower bound of $Ω(nε^{-2}\log(1/δ))$ when the learner is forced to play just duels instead of larger subsetwise queries. Further, we extend the results to a more general `\emph{noisy Block-Rank}' model, which ensures robustness of our techniques. Overall, our results justify the advantage of playing subsetwise queries over pairwise preferences $(k=2)$, we show the latter provably fails to exploit correlation.