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

By Suprovat Ghoshal, Aadirupa Saha. 2022

13 citations recorded by the source corpus.

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 $(\epsilon,\delta)$-PAC learnable with only $O(r \epsilon^{-2} \log(n/\delta))$ samples. This improves on the standard sample complexity bound of $\tilde{O}(n\epsilon^{-2} \log(1/\delta))$ 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 $\Omega(n\epsilon^{-2}\log(1/\delta))$ 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.

Subfields: Artificial Intelligence, Computer Networks and Communications, Management Science and Operations Research, Reinforcement Learning

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Citations in the corpus

Dueling RL: Reinforcement Learning with Trajectory Preferences (2021, background): “Yue and Joachims (2009, 2011); Saha and Krishnamurthy (2022); Ghoshal and Saha (2022); Saha and Gopalan (2018a) The setting is relevant in various realworld systems which aim to collect information from user preferences, including recommender systems, retail management, search engine optimization,…”
Principled Reinforcement Learning with Human Feedback from Pairwise or K-wise Comparisons (2023, background): “In the literature of dueling bandit, one compares two actions and aims to minimize regret based on pairwise comparisons (Yue et al., 2012; Zoghi et al., 2014b; Yue and Joachims, 2009; 2011; Saha and Krishnamurthy, 2022; Ghoshal and Saha, 2022; Saha and Gopalan, 2018a; Ailon et al., 2014; Zoghi et al”