Online Preselection with Context Information under the Plackett-Luce Model

Abstract

We consider an extension of the contextual multi-armed bandit problem, in which, instead of selecting a single alternative (arm), a learner is supposed to make a preselection in the form of a subset of alternatives. More specifically, in each iteration, the learner is presented a set of arms and a context, both described in terms of feature vectors. The task of the learner is to preselect $k$ of these arms, among which a final choice is made in a second step. In our setup, we assume that each arm has a latent (context-dependent) utility, and that feedback on a preselection is produced according to a Plackett-Luce model. We propose the CPPL algorithm, which is inspired by the well-known UCB algorithm, and evaluate this algorithm on synthetic and real data. In particular, we consider an online algorithm selection scenario, which served as a main motivation of our problem setting. Here, an instance (which defines the context) from a certain problem class (such as SAT) can be solved by different algorithms (the arms), but only $k$ of these algorithms can actually be run.

References in corpus (10)

• A Contextual-Bandit Approach to Personalized News Article Recommendation
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• Dynamic Assortment Optimization with Changing Contextual Information
• Contextual Dueling Bandits
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• PAC Ranking from Pairwise and Listwise Queries: Lower Bounds and Upper Bounds
• Automated Algorithm Selection: Survey and Perspectives
• Active Ranking with Subset-wise Preferences

Cited by in corpus (2)

• Learning How to Optimize Black-Box Functions With Extreme Limits on the Number of Function Evaluations
• Learning to Rank under Multinomial Logit Choice