Bandits with Anytime Knapsacks

Eray Can Elumar, Cem Tekin, Osman Yagan

Keywords: multi-armed bandits, knapsack problem, online learning

Abstract:

We consider bandits with anytime knapsacks (BwAK), a novel version of the BwK problem where there is an anytime cost constraint instead of a total cost budget. This problem setting introduces additional complexities as it mandates adherence to the constraint throughout the decision-making process. We propose SUAK, an algorithm that utilizes upper confidence bounds to identify the optimal mixture of arms while maintaining a balance between exploration and exploitation. SUAK is an adaptive algorithm that strategically utilizes the available budget in each round in the decision-making process and skips a round when it is possible to violate the anytime cost constraint. In particular, SUAK slightly under-utilizes the available cost budget to reduce the need for skipping rounds. We show that SUAK attains the same problem-dependent regret upper bound of $ O(K \log T)$ established in prior work under the simpler BwK framework. Finally, we provide simulations to verify the utility of SUAK in practical settings.

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Submission Number: 8175