Leveraging (Biased) Information: Multi-armed Bandits with Offline Data

Published: 02 May 2024, Last Modified: 25 Jun 2024ICML 2024 SpotlightEveryoneRevisionsBibTeXCC BY 4.0
Abstract: We leverage offline data to facilitate online learning in stochastic multi-armed bandits. The probability distributions that govern the offline data and the online rewards can be different. Without any non-trival upper bound on their difference, we show that no non-anticipatory policy can out-perform the UCB policy by (Auer et al. 2002), even in the presence of offline data. In complement, we propose an online policy MIN-UCB, which outperforms UCB when a non-trivial upper bound is given. MIN-UCB adaptively chooses to utilize the offline data when they are deemed informative, and to ignore them otherwise. MIN-UCB is shown to be tight in terms of both instance indepedent and dependent regret bounds. Finally, we corroborate the theoretical results with numerical experiments.
Submission Number: 5194
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