An efficient algorithm for contextual bandits with knapsacks, and an extension to concave objectives
This work addresses a computational bottleneck in resource-constrained decision-making for applications like online advertising or resource allocation, providing an efficient solution with improved theoretical guarantees.
The authors tackled the problem of contextual multi-armed bandits with global knapsack constraints by developing a computationally efficient algorithm that achieves slightly better regret bounds than prior work, answering an open question from Badanidiyuru et al. (2014). They also extended the results to handle concave objectives without knapsack constraints.
We consider a contextual version of multi-armed bandit problem with global knapsack constraints. In each round, the outcome of pulling an arm is a scalar reward and a resource consumption vector, both dependent on the context, and the global knapsack constraints require the total consumption for each resource to be below some pre-fixed budget. The learning agent competes with an arbitrary set of context-dependent policies. This problem was introduced by Badanidiyuru et al. (2014), who gave a computationally inefficient algorithm with near-optimal regret bounds for it. We give a computationally efficient algorithm for this problem with slightly better regret bounds, by generalizing the approach of Agarwal et al. (2014) for the non-constrained version of the problem. The computational time of our algorithm scales logarithmically in the size of the policy space. This answers the main open question of Badanidiyuru et al. (2014). We also extend our results to a variant where there are no knapsack constraints but the objective is an arbitrary Lipschitz concave function of the sum of outcome vectors.