Saturation-Insensitive Dueling Bandits with General Function Approximation

Abstract:We study contextual dueling bandits with general function approximation under the Bradley-Terry-Luce (BTL) preference model. A key challenge in this setting is the saturation of the preference model: when the current reward model can already distinguish two actions with high confidence, the resulting preference feedback becomes weakly informative, making it difficult to further improve reward estimation. Consequently, existing sample-complexity analyses often depend on the inverse-derivative factor $1 / \sigma'[\Delta_{r^\ast}]$ which can be prohibitively large when the link function $\sigma$ saturates for large reward gaps $\Delta_{r^\ast}$. To address this issue, we introduce `SI-CDB`, an algorithm that selects opponent arms using a carefully designed heuristic for arm selection. This design enables saturation-insensitive reward learning and recovers the near-optimal dependence for linear reward classes, eliminating the unfavorable $1/\sigma'(\cdot)$ factor. The core of our analysis is a localized Eluder dimension framework tailored to dueling bandits with general function approximation. Our theoretical results also explain why two-arm regret analysis is crucial for improving single-arm performance in dueling bandits.

Machine Learning (cs.LG)

arXiv:2609.33011 [cs.LG]

(or arXiv:2609.33011v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.33011 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.