Clustered Linear Contextual Bandits with Knapsacks
This addresses resource-constrained decision-making in multi-armed bandit settings, such as online advertising or resource allocation, but is incremental as it builds on existing bandit and econometric techniques.
The paper tackles the problem of maximizing total reward in clustered linear contextual bandits with knapsack constraints, where cluster memberships are unknown, by developing an algorithm that achieves sublinear regret without needing access to all arms, using a one-time clustering on a random subset.
In this work, we study clustered contextual bandits where rewards and resource consumption are the outcomes of cluster-specific linear models. The arms are divided in clusters, with the cluster memberships being unknown to an algorithm. Pulling an arm in a time period results in a reward and in consumption for each one of multiple resources, and with the total consumption of any resource exceeding a constraint implying the termination of the algorithm. Thus, maximizing the total reward requires learning not only models about the reward and the resource consumption, but also cluster memberships. We provide an algorithm that achieves regret sublinear in the number of time periods, without requiring access to all of the arms. In particular, we show that it suffices to perform clustering only once to a randomly selected subset of the arms. To achieve this result, we provide a sophisticated combination of techniques from the literature of econometrics and of bandits with constraints.