# Best Arm Identification in Generalized Linear Bandits via Hybrid Feedback

arXiv: https://arxiv.org/abs/2605.05745 · HTML: https://mlsanity.com/paper/2605.05745/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 32 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 17 of 17)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [On the Complexity of Best Arm Identification in Multi-Armed Bandit Models](https://mlsanity.com/paper/1407.4443/) (2014)
- [Optimal Best Arm Identification with Fixed Confidence](https://mlsanity.com/paper/1602.04589/) (2016)
- [Best-Arm Identification in Linear Bandits](https://mlsanity.com/paper/1409.6110/) (2014)
- [Optimal Best-arm Identification in Linear Bandits](https://mlsanity.com/paper/2006.16073/) (2020)
- [Gamification of Pure Exploration for Linear Bandits](https://mlsanity.com/paper/2007.00953/) (2020)
- [Conversational Contextual Bandit: Algorithm and Application](https://mlsanity.com/paper/1906.01219/) (2019)
- [Improved Confidence Bounds for the Linear Logistic Model and Applications to Linear Bandits](https://mlsanity.com/paper/2011.11222/) (2020)
- [Self-Concordant Analysis of Generalized Linear Bandits with Forgetting](https://mlsanity.com/paper/2011.00819/) (2020)
- [A Unified Confidence Sequence for Generalized Linear Models, with Applications to Bandits](https://mlsanity.com/paper/2407.13977/) (2024)
- [Best Arm Identification in Generalized Linear Bandits](https://mlsanity.com/paper/1905.08224/) (2019)
- [Confidence Sequences for Generalized Linear Models via Regret Analysis](https://mlsanity.com/paper/2504.16555/) (2025)
- [Confidence Estimation via Sequential Likelihood Mixing](https://mlsanity.com/paper/2502.14689/) (2025)
- [Conversational Dueling Bandits in Generalized Linear Models](https://mlsanity.com/paper/2407.18488/) (2024)
- [Near Optimal Pure Exploration in Logistic Bandits](https://mlsanity.com/paper/2410.20640/) (2024)
- [Fusing Reward and Dueling Feedback in Stochastic Bandits](https://mlsanity.com/paper/2504.15812/) (2025)

## Built on by (most cited first, 1 of 1)

- [Gaussian Process Bandits for AI System Optimization with Selectively Verified Feedback](https://mlsanity.com/paper/2610.17760/) (2026)

## Abstract (arXiv)

We study fixed-confidence best arm identification in generalized linear bandits under a hybrid feedback model: at each round, the learner may query either (i) absolute reward feedback from a single arm or (ii) relative (dueling) feedback from an arm pair, both governed by generalized linear models. We introduce a likelihood-ratio--based confidence sequence that unifies heterogeneous generalized linear observations and yields an explicit ellipsoidal confidence set under a self-concordance assumption. Building on this confidence set, we propose a hybrid Track-and-Stop algorithm that adaptively allocates queries by tracking a minimax-optimal design over a joint action space of arms and pairs. We establish δ-correctness and provide high-probability upper bounds on the stopping time. We further extend the framework to a cost-aware setting that accounts for heterogeneous acquisition costs across feedback modalities. Empirical experiments demonstrate that the proposed algorithms significantly improve sample efficiency over baseline methods.