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There is a rising interest in industrial online applications where databecomes available sequentially. Inspired by the recommendation of playlists tousers where their preferences can be collected during the listening of theentire playlist, we study a novel bandit setting, namely Multi-Armed Banditwith Temporally-Partitioned Rewards (TP-MAB), in which the stochastic rewardassociated with the pull of an arm is partitioned over a finite number ofconsecutive rounds following the pull. This setting, unexplored so far to thebest of our knowledge, is a natural extension of delayed-feedback bandits tothe case in which rewards may be dilated over a finite-time span after the pullinstead of being fully disclosed in a single, potentially delayed round. Weprovide two algorithms to address TP-MAB problems, namely, TP-UCB-FR andTP-UCB-EW, which exploit the partial information disclosed by the rewardcollected over time. We show that our algorithms provide better asymptoticalregret upper bounds than delayed-feedback bandit algorithms when a propertycharacterizing a broad set of reward structures of practical interest, namelyalpha-smoothness, holds. We also empirically evaluate their performance acrossa wide range of settings, both synthetically generated and from a real-worldmedia recommendation problem.

Multi-Armed Bandit Problem with Temporally-Partitioned Rewards: When Partial Feedback Counts