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We consider a contextual version of multi-armed bandit problem with globalknapsack constraints. In each round, the outcome of pulling an arm is a scalarreward and a resource consumption vector, both dependent on the context, andthe global knapsack constraints require the total consumption for each resourceto be below some pre-fixed budget. The learning agent competes with anarbitrary set of context-dependent policies. This problem was introduced byBadanidiyuru et al. (2014), who gave a computationally inefficient algorithmwith near-optimal regret bounds for it. We give a computationally efficientalgorithm for this problem with slightly better regret bounds, by generalizingthe approach of Agarwal et al. (2014) for the non-constrained version of theproblem. The computational time of our algorithm scales logarithmically in thesize of the policy space. This answers the main open question of Badanidiyuruet al. (2014). We also extend our results to a variant where there are noknapsack constraints but the objective is an arbitrary Lipschitz concavefunction of the sum of outcome vectors.

An efficient algorithm for contextual bandits with knapsacks, and an extension to concave objectives