# Safe Convex Learning under Uncertain Constraints

arXiv: https://arxiv.org/abs/1903.04626 · HTML: https://mlsanity.com/paper/1903.04626/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2019.

## Built on by (most cited first, 17 of 17)

- [How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Review](https://mlsanity.com/paper/2107.12045/) (2021)
- [DOPE: Doubly Optimistic and Pessimistic Exploration for Safe Reinforcement Learning](https://mlsanity.com/paper/2112.00885/) (2021)
- [Diffusion Models as Constrained Samplers for Optimization with Unknown Constraints](https://mlsanity.com/paper/2402.18012/) (2024)
- [An Efficient Pessimistic-Optimistic Algorithm for Stochastic Linear Bandits with General Constraints](https://mlsanity.com/paper/2102.05295/) (2021)
- [Multi-channel Autobidding with Budget and ROI Constraints](https://mlsanity.com/paper/2302.01523/) (2023)
- [Safe Online Convex Optimization with Unknown Linear Safety Constraints](https://mlsanity.com/paper/2111.07430/) (2021)
- [Learning to Persuade on the Fly: Robustness Against Ignorance](https://mlsanity.com/paper/2102.10156/) (2021)
- [Log Barriers for Safe Black-box Optimization with Application to Safe Reinforcement Learning](https://mlsanity.com/paper/2207.10415/) (2022)
- [Directional Optimism for Safe Linear Bandits](https://mlsanity.com/paper/2308.15006/) (2023)
- [Dynamic Regret Analysis of Safe Distributed Online Optimization for Convex and Non-convex Problems](https://mlsanity.com/paper/2302.12320/) (2023)
- [Price of Safety in Linear Best Arm Identification](https://mlsanity.com/paper/2309.08709/) (2023)
- [The Impact of the Geometric Properties of the Constraint Set in Safe Optimization with Bandit Feedback](https://mlsanity.com/paper/2305.00889/) (2023)
- [Online Learning with Unknown Constraints](https://mlsanity.com/paper/2403.04033/) (2024)
- [Safe Linear Leveling Bandits](https://mlsanity.com/paper/2112.06728/) (2021)
- [Optimistic Safety for Online Convex Optimization with Unknown Linear Constraints](https://mlsanity.com/paper/2403.05786/) (2024)
- [Safe Online Convex Optimization with Multi-Point Feedback](https://mlsanity.com/paper/2407.11471/) (2024)
- [Constrained Online Learning with Noisy Constraint Values](https://mlsanity.com/paper/2609.06921/) (2026)

## Abstract (arXiv)

We address the problem of minimizing a convex smooth function f(x) over a compact polyhedral set D given a stochastic zeroth-order constraint feedback model. This problem arises in safety-critical machine learning applications, such as personalized medicine and robotics. In such cases, one needs to ensure constraints are satisfied while exploring the decision space to find optimum of the loss function. We propose a new variant of the Frank-Wolfe algorithm, which applies to the case of uncertain linear constraints. Using robust optimization, we provide the convergence rate of the algorithm while guaranteeing feasibility of all iterates, with high probability.