Clustered Linear Contextual Bandits with Knapsacks

TL;DR

This paper introduces a novel clustered linear contextual bandit algorithm that efficiently learns cluster memberships and resource models, achieving sublinear regret while respecting resource constraints, with only a single clustering step on a subset of arms.

Contribution

It proposes a new algorithm for clustered contextual bandits with knapsack constraints that requires only one clustering step, combining econometrics and bandit techniques.

Findings

Achieves sublinear regret in resource-constrained clustered bandits.

Requires clustering only once on a subset of arms.

Effectively balances reward maximization and resource constraints.

Abstract

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.