# Active Learning with Safety Constraints

arXiv: https://arxiv.org/abs/2206.11183 · HTML: https://mlsanity.com/paper/2206.11183/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 47 references that are in the map.
- First posted on arXiv 22 Jun 2022.

## Builds on (most cited first, 24 of 24)

- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [On the Complexity of Best Arm Identification in Multi-Armed Bandit Models](https://mlsanity.com/paper/1407.4443/) (2014)
- [lil' UCB : An Optimal Exploration Algorithm for Multi-Armed Bandits](https://mlsanity.com/paper/1312.7308/) (2013)
- [Best-Arm Identification in Linear Bandits](https://mlsanity.com/paper/1409.6110/) (2014)
- [Sequential Experimental Design for Transductive Linear Bandits](https://mlsanity.com/paper/1906.08399/) (2019)
- [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)
- [Randomized Exploration in Generalized Linear Bandits](https://mlsanity.com/paper/1906.08947/) (2019)
- [Stochastic Bandits with Linear Constraints](https://mlsanity.com/paper/2006.10185/) (2020)
- [Gamification of Pure Exploration for Linear Bandits](https://mlsanity.com/paper/2007.00953/) (2020)
- [Conservative Contextual Linear Bandits](https://mlsanity.com/paper/1611.06426/) (2016)
- [High-Dimensional Experimental Design and Kernel Bandits](https://mlsanity.com/paper/2105.05806/) (2021)
- [Training Well-Generalizing Classifiers for Fairness Metrics and Other Data-Dependent Constraints](https://mlsanity.com/paper/1807.00028/) (2018)
- [Reward-Free RL is No Harder Than Reward-Aware RL in Linear Markov Decision Processes](https://mlsanity.com/paper/2201.11206/) (2022)
- [An Empirical Process Approach to the Union Bound: Practical Algorithms for Combinatorial and Linear Bandits](https://mlsanity.com/paper/2006.11685/) (2020)
- [Fully adaptive algorithm for pure exploration in linear bandits](https://mlsanity.com/paper/1710.05552/) (2017)
- [Safe Linear Thompson Sampling with Side Information](https://mlsanity.com/paper/1911.02156/) (2019)
- [The Simulator: Understanding Adaptive Sampling in the Moderate-Confidence Regime](https://mlsanity.com/paper/1702.05186/) (2017)
- [Stage-wise Conservative Linear Bandits](https://mlsanity.com/paper/2010.00081/) (2020)
- [Best Arm Identification with Safety Constraints](https://mlsanity.com/paper/2111.12151/) (2021)
- [Nearly Optimal Algorithms for Level Set Estimation](https://mlsanity.com/paper/2111.01768/) (2021)
- [Improved Algorithms for Agnostic Pool-based Active Classification](https://mlsanity.com/paper/2105.06499/) (2021)
- [A New Perspective on Pool-Based Active Classification and False-Discovery Control](https://mlsanity.com/paper/2008.06555/) (2020)
- [Selective Sampling for Online Best-arm Identification](https://mlsanity.com/paper/2110.14864/) (2021)

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

- [Learning Safety Constraints from Demonstrations with Unknown Rewards](https://mlsanity.com/paper/2305.16147/) (2023)
- [Safe Linear Bandits over Unknown Polytopes](https://mlsanity.com/paper/2209.13694/) (2022)
- [Pure Exploration in Bandits with Linear Constraints](https://mlsanity.com/paper/2306.12774/) (2023)
- [Directional Optimism for Safe Linear Bandits](https://mlsanity.com/paper/2308.15006/) (2023)
- [Multitask Learning with No Regret: from Improved Confidence Bounds to Active Learning](https://mlsanity.com/paper/2308.01744/) (2023)
- [SaVeR: Optimal Data Collection Strategy for Safe Policy Evaluation in Tabular MDP](https://mlsanity.com/paper/2406.02165/) (2024)
- [Testing the Feasibility of Linear Programs with Bandit Feedback](https://mlsanity.com/paper/2406.15648/) (2024)
- [Fair Active Learning in Low-Data Regimes](https://mlsanity.com/paper/2312.08559/) (2023)
- [Pure Exploration for Constrained Best Mixed Arm Identification with a Fixed Budget](https://mlsanity.com/paper/2405.15090/) (2024)
- [Asymptotically Optimal Linear Best Feasible Arm Identification with Fixed Budget](https://mlsanity.com/paper/2506.02386/) (2025)
- [Multi-Metric Adaptive Experimental Design Under a Fixed Budget with Validation](https://mlsanity.com/paper/2506.03062/) (2025)
- [Incentivized Collaboration in Active Learning](https://mlsanity.com/paper/2311.00260/) (2023)
- [Learning to Explore with Lagrangians for Bandits under Unknown Linear Constraints](https://mlsanity.com/paper/2410.18844/) (2024)
- [Constrained Linear Thompson Sampling](https://mlsanity.com/paper/2503.02043/) (2025)
- [Latent Order Bandits](https://mlsanity.com/paper/2605.07304/) (2026)
- [Multi-Task Representation Learning for Conservative Linear Bandits](https://mlsanity.com/paper/2605.12176/) (2026)

## Abstract (arXiv)

Active learning methods have shown great promise in reducing the number of samples necessary for learning. As automated learning systems are adopted into real-time, real-world decision-making pipelines, it is increasingly important that such algorithms are designed with safety in mind. In this work we investigate the complexity of learning the best safe decision in interactive environments. We reduce this problem to a constrained linear bandits problem, where our goal is to find the best arm satisfying certain (unknown) safety constraints. We propose an adaptive experimental design-based algorithm, which we show efficiently trades off between the difficulty of showing an arm is unsafe vs suboptimal. To our knowledge, our results are the first on best-arm identification in linear bandits with safety constraints. In practice, we demonstrate that this approach performs well on synthetic and real world datasets.