# Thresholding Bandit for Dose-ranging: The Impact of Monotonicity

arXiv: https://arxiv.org/abs/1711.04454 · HTML: https://mlsanity.com/paper/1711.04454/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2017.

## Built on by (most cited first, 16 of 16)

- [Best Arm Identification with Safety Constraints](https://mlsanity.com/paper/2111.12151/) (2021)
- [Sequential Learning of the Pareto Front for Multi-objective Bandits](https://mlsanity.com/paper/2501.17513/) (2025)
- [SDF-Bayes: Cautious Optimism in Safe Dose-Finding Clinical Trials with Drug Combinations and Heterogeneous Patient Groups](https://mlsanity.com/paper/2101.10998/) (2021)
- [Multi-armed Bandit Requiring Monotone Arm Sequences](https://mlsanity.com/paper/2106.03790/) (2021)
- [Problem Dependent View on Structured Thresholding Bandit Problems](https://mlsanity.com/paper/2106.10166/) (2021)
- [Online Sign Identification: Minimization of the Number of Errors in Thresholding Bandits](https://mlsanity.com/paper/2110.09133/) (2021)
- [Measurement-based Admission Control in Sliced Networks: A Best Arm Identification Approach](https://mlsanity.com/paper/2204.06910/) (2022)
- [LinearAPT: An Adaptive Algorithm for the Fixed-Budget Thresholding Linear Bandit Problem](https://mlsanity.com/paper/2403.06230/) (2024)
- [Pure Exploration under Mediators' Feedback](https://mlsanity.com/paper/2308.15552/) (2023)
- [Fixed-Confidence Multiple Change Point Identification under Bandit Feedback](https://mlsanity.com/paper/2507.08994/) (2025)
- [Non-Asymptotic Best Policy Identification Guarantees in Online Reinforcement Learning](https://mlsanity.com/paper/2607.17201/) (2026)
- [An Asymptotically Optimal Algorithm for the Convex Hull Membership Problem](https://mlsanity.com/paper/2302.02033/) (2023)
- [Markdown Pricing Under an Unknown Parametric Demand Model](https://mlsanity.com/paper/2312.15286/) (2023)
- [Learning to Explore with Lagrangians for Bandits under Unknown Linear Constraints](https://mlsanity.com/paper/2410.18844/) (2024)
- [Locally Differentially Private Thresholding Bandits](https://mlsanity.com/paper/2507.23073/) (2025)
- [Threshold-Based Optimal Arm Selection in Monotonic Bandits: Regret Lower Bounds and Algorithms](https://mlsanity.com/paper/2509.02119/) (2025)

## Abstract (arXiv)

We analyze the sample complexity of the thresholding bandit problem, with and without the assumption that the mean values of the arms are increasing. In each case, we provide a lower bound valid for any risk δ and any δ-correct algorithm; in addition, we propose an algorithm whose sample complexity is of the same order of magnitude for small risks. This work is motivated by phase 1 clinical trials, a practically important setting where the arm means are increasing by nature, and where no satisfactory solution is available so far.