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We consider a resource-aware variant of the classical multi-armed banditproblem: In each round, the learner selects an arm and determines a resourcelimit. It then observes a corresponding (random) reward, provided the (random)amount of consumed resources remains below the limit. Otherwise, theobservation is censored, i.e., no reward is obtained. For this problem setting,we introduce a measure of regret, which incorporates the actual amount ofallocated resources of each learning round as well as the optimality ofrealizable rewards. Thus, to minimize regret, the learner needs to set aresource limit and choose an arm in such a way that the chance to realize ahigh reward within the predefined resource limit is high, while the resourcelimit itself should be kept as low as possible. We propose a UCB-inspiredonline learning algorithm, which we analyze theoretically in terms of itsregret upper bound. In a simulation study, we show that our learning algorithmoutperforms straightforward extensions of standard multi-armed banditalgorithms.

Multi-Armed Bandits with Censored Consumption of Resources