# Elicitation and Decision Geometry in Single-Index Bandits

arXiv: https://arxiv.org/abs/2609.35622 · HTML: https://mlsanity.com/paper/2609.35622/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 30 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 9 of 9)

- [Mostly Exploration-Free Algorithms for Contextual Bandits](https://mlsanity.com/paper/1704.09011/) (2017)
- [Misspecified Linear Bandits](https://mlsanity.com/paper/1704.06880/) (2017)
- [Self-Concordant Analysis of Generalized Linear Bandits with Forgetting](https://mlsanity.com/paper/2011.00819/) (2020)
- [Generalized Linear Bandits: Almost Optimal Regret with One-Pass Update](https://mlsanity.com/paper/2507.11847/) (2025)
- [Local Anti-Concentration Class: Logarithmic Regret for Greedy Linear Contextual Bandit](https://mlsanity.com/paper/2411.12878/) (2024)
- [Single Index Bandits: Generalized Linear Contextual Bandits with Unknown Reward Functions](https://mlsanity.com/paper/2506.12751/) (2025)
- [Batched Single-Index Global Multi-Armed Bandits with Covariates](https://mlsanity.com/paper/2503.00565/) (2025)
- [Relative Contrast Estimation and Inference for Treatment Recommendation](https://mlsanity.com/paper/2010.13904/) (2020)
- [Kernel Single-Index Bandits: Estimation, Inference, and Learning](https://mlsanity.com/paper/2603.18938/) (2026)

## Abstract (arXiv)

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.