# Convex Methods for Constrained Linear Bandits

arXiv: https://arxiv.org/abs/2311.04338 · HTML: https://mlsanity.com/paper/2311.04338/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 16 references that are in the map.
- First posted on arXiv 7 Nov 2023.

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

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Linear Stochastic Bandits Under Safety Constraints](https://mlsanity.com/paper/1908.05814/) (2019)
- [Stochastic Bandits with Linear Constraints](https://mlsanity.com/paper/2006.10185/) (2020)
- [Conservative Contextual Linear Bandits](https://mlsanity.com/paper/1611.06426/) (2016)
- [Safe Linear Thompson Sampling with Side Information](https://mlsanity.com/paper/1911.02156/) (2019)
- [Stage-wise Conservative Linear Bandits](https://mlsanity.com/paper/2010.00081/) (2020)
- [Safe Linear Stochastic Bandits](https://mlsanity.com/paper/1911.09501/) (2019)
- [Strategies for Safe Multi-Armed Bandits with Logarithmic Regret and Risk](https://mlsanity.com/paper/2204.00706/) (2022)
- [The Impact of the Geometric Properties of the Constraint Set in Safe Optimization with Bandit Feedback](https://mlsanity.com/paper/2305.00889/) (2023)

## Built on by (most cited first, 5 of 5)

- [Provably Efficient RL for Linear MDPs under Instantaneous Safety Constraints in Non-Convex Feature Spaces](https://mlsanity.com/paper/2502.18655/) (2025)
- [Cooperative Multi-Agent Constrained Stochastic Linear Bandits](https://mlsanity.com/paper/2410.17382/) (2024)
- [Multi-Agent Stage-wise Conservative Linear Bandits](https://mlsanity.com/paper/2510.00602/) (2025)
- [On-Policy Distillation of Language Models for Autonomous Vehicle Motion Planning](https://mlsanity.com/paper/2604.07944/) (2026)
- [Constrained Linear Thompson Sampling](https://mlsanity.com/paper/2503.02043/) (2025)

## Abstract (arXiv)

Recently, bandit optimization has received significant attention in real-world safety-critical systems that involve repeated interactions with humans. While there exist various algorithms with performance guarantees in the literature, practical implementation of the algorithms has not received as much attention. This work presents a comprehensive study on the computational aspects of safe bandit algorithms, specifically safe linear bandits, by introducing a framework that leverages convex programming tools to create computationally efficient policies. In particular, we first characterize the properties of the optimal policy for safe linear bandit problem and then propose an end-to-end pipeline of safe linear bandit algorithms that only involves solving convex problems. We also numerically evaluate the performance of our proposed methods.