# Safe Linear Leveling Bandits

arXiv: https://arxiv.org/abs/2112.06728 · HTML: https://mlsanity.com/paper/2112.06728/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 39 references that are in the map.
- First posted on arXiv 13 Dec 2021.

## Builds on (most cited first, 13 of 13)

- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [Multi-armed Bandit Models for the Optimal Design of Clinical Trials: Benefits and Challenges](https://mlsanity.com/paper/1507.08025/) (2015)
- [Ethical Machine Learning in Health Care](https://mlsanity.com/paper/2009.10576/) (2020)
- [Linear Stochastic Bandits Under Safety Constraints](https://mlsanity.com/paper/1908.05814/) (2019)
- [Stagewise Safe Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1806.07555/) (2018)
- [Safe Exploration for Interactive Machine Learning](https://mlsanity.com/paper/1910.13726/) (2019)
- [Safe Linear Thompson Sampling with Side Information](https://mlsanity.com/paper/1911.02156/) (2019)
- [On Multi-Armed Bandit Designs for Dose-Finding Clinical Trials](https://mlsanity.com/paper/1903.07082/) (2019)
- [Safe Linear Stochastic Bandits](https://mlsanity.com/paper/1911.09501/) (2019)
- [Basal Glucose Control in Type 1 Diabetes using Deep Reinforcement Learning: An In Silico Validation](https://mlsanity.com/paper/2005.09059/) (2020)
- [Safe Convex Learning under Uncertain Constraints](https://mlsanity.com/paper/1903.04626/) (2019)
- [Learning for Dose Allocation in Adaptive Clinical Trials with Safety Constraints](https://mlsanity.com/paper/2006.05026/) (2020)
- [Contextual Constrained Learning for Dose-Finding Clinical Trials](https://mlsanity.com/paper/2001.02463/) (2020)

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

- [Robust Best-arm Identification in Linear Bandits](https://mlsanity.com/paper/2311.04731/) (2023)

## Abstract (arXiv)

Multi-armed bandits (MAB) are extensively studied in various settings where the objective is to textitmaximize the actions' outcomes (i.e., rewards) over time. Since safety is crucial in many real-world problems, safe versions of MAB algorithms have also garnered considerable interest. In this work, we tackle a different critical task through the lens of textitlinear stochastic bandits, where the aim is to keep the actions' outcomes close to a target level while respecting a textittwo-sided safety constraint, which we call textitleveling. Such a task is prevalent in numerous domains. Many healthcare problems, for instance, require keeping a physiological variable in a range and preferably close to a target level. The radical change in our objective necessitates a new acquisition strategy, which is at the heart of a MAB algorithm. We propose SALE-LTS: Safe Leveling via Linear Thompson Sampling algorithm, with a novel acquisition strategy to accommodate our task and show that it achieves sublinear regret with the same time and dimension dependence as previous works on the classical reward maximization problem absent any safety constraint. We demonstrate and discuss our algorithm's empirical performance in detail via thorough experiments.