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