Lipschitz Dueling Bandits over Continuous Action Spaces

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Abstract:We study for the first time, stochastic dueling bandits over continuous action spaces with Lipschitz structure, where feedback is purely comparative. While dueling bandits and Lipschitz bandits have been studied separately, their combination has remained unexplored. We propose the first algorithm for Lipschitz dueling bandits, using round-based exploration and recursive region elimination guided by an adaptive reference arm. We develop new analytical tools for relative feedback and prove a regret bound of $\tilde O\left(T^{\frac{d_z+1}{d_z+2}}\right)$, where $d_z$ is the zooming dimension of the near-optimal region. Further, our algorithm takes only logarithmic space in terms of the total time horizon, best achievable by any bandit algorithm over a continuous action space.

Subjects:

Machine Learning (cs.LG); Information Retrieval (cs.IR); Multiagent Systems (cs.MA)

Cite as: arXiv:2604.00523 [cs.LG]

(or arXiv:2604.00523v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2604.00523

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Shweta Jain [view email] [v1] Wed, 1 Apr 2026 06:07:33 UTC (50 KB)