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