Elicitation and Decision Geometry in Single-Index Bandits

Abstract:We study two-arm contextual bandits with arm-specific single indices and a shared unknown monotone link. Monotonicity makes the optimal action depend only on the contrast between the index directions, hence arm-specific reward functions need not be estimated. We introduce Natural Boundary Learning (NBL), a greedy procedure that uses a sequential Stein contrast to learn the optimal boundary directly, without estimating the reward functions or the common link. We characterize the local Riemannian dynamics of NBL through a decision stability coefficient balancing arm separation, link geometry, and the context distribution. We show that this stability is connected to the elicitation geometry of the underlying convex potential. Under local decision stability, NBL contracts toward the optimal boundary and achieves $O(\log n)$ expected regret. Numerical experiments illustrate the predicted stability regimes and compare NBL with a parametric greedy benchmark under link misspecification.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2609.35622 [stat.ML]

(or arXiv:2609.35622v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2609.35622 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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