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.
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BibTeX
@misc{arya2026elicitation,
title = {{Elicitation and Decision Geometry in Single-Index Bandits}},
author = {Sakshi Arya and Cheng Soon Ong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35622},
eprint = {2609.35622},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35622},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Elicitation and Decision Geometry in Single-Index Bandits
AU - Sakshi Arya
AU - Cheng Soon Ong
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35622
UR - https://arxiv.org/abs/2609.35622
AB - 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.
ER -