Learning Across the Gap: Hybrid Multi-armed Bandits with Heterogeneous Offline and Online Data

The multi-armed bandit (MAB) is a fundamental online decision-making framework that has been extensively studied over the past two decades. To mitigate the high cost and slow convergence of purely online learning, modern MAB approaches have explored hybrid paradigms that leverage offline data to warm-start online learning. However, existing approaches face a significant limitation by assuming that the offline and online data are homogeneous—they share the same feedback structure and are drawn from the same underlying distribution. This assumption is often violated in practice, where offline data often originate from diverse sources and evolving environments, resulting in feedback heterogeneity and distributional shifts. In this work, we tackle the challenge of learning across this offline-online gap by developing a general hybrid bandit framework that incorporates heterogeneous offline data to improve online performance. We study two hybrid settings: (1) using reward-based offline data to accelerate online learning in preference-based bandits (i.e., dueling bandits), and (2) using preference-based offline data to improve online standard MAB algorithms. For both settings, we design novel algorithms and derive tight regret bounds that match or improve upon existing benchmarks despite heterogeneity. Empirical evaluations on both synthetic and real-world datasets show that our proposed methods significantly outperform baseline algorithms.