mlsanityData to 7 Oct 2026

Safe Convex Learning under Uncertain Constraints

arXiv 1903.04626 ↗First posted 11 Mar 2019math.OCcited by 17

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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.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Mar 2019.

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Citing papers per year: 2021: 6; 2022: 1; 2023: 5; 2024: 4; 2025: 0; 2026: 1.

17 papers.

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  1. 2021How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Reviewcited by 36
  2. 2021DOPE: Doubly Optimistic and Pessimistic Exploration for Safe Reinforcement Learningcited by 34
  3. 2024Diffusion Models as Constrained Samplers for Optimization with Unknown Constraintscited by 33
  4. 2021An Efficient Pessimistic-Optimistic Algorithm for Stochastic Linear Bandits with General Constraintscited by 29
  5. 2023Multi-channel Autobidding with Budget and ROI Constraintscited by 14
  6. 2021Safe Online Convex Optimization with Unknown Linear Safety Constraintscited by 13
  7. 2021Learning to Persuade on the Fly: Robustness Against Ignorancecited by 12
  8. 2022Log Barriers for Safe Black-box Optimization with Application to Safe Reinforcement Learningcited by 11
  9. 2023Directional Optimism for Safe Linear Banditscited by 8
  10. 2023Dynamic Regret Analysis of Safe Distributed Online Optimization for Convex and Non-convex Problemscited by 4
  11. 2023Price of Safety in Linear Best Arm Identificationcited by 4
  12. 2023The Impact of the Geometric Properties of the Constraint Set in Safe Optimization with Bandit Feedbackcited by 3
5 more
  1. 2024Online Learning with Unknown Constraintscited by 2
  2. 2021Safe Linear Leveling Banditscited by 1
  3. 2024Optimistic Safety for Online Convex Optimization with Unknown Linear Constraintscited by 1
  4. 2024Safe Online Convex Optimization with Multi-Point Feedbackcited by 0
  5. 2026Constrained Online Learning with Noisy Constraint Valuescited by 0