mlsanityData to 14 Oct 2026

The Impact of the Geometric Properties of the Constraint Set in Safe Optimization with Bandit Feedback

arXiv 2305.00889 ↗First posted 1 May 2023cs.LG math.OCcited by 3

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Abstract (arXiv)

We consider a safe optimization problem with bandit feedback in which an agent sequentially chooses actions and observes responses from the environment, with the goal of maximizing an arbitrary function of the response while respecting stage-wise constraints. We propose an algorithm for this problem, and study how the geometric properties of the constraint set impact the regret of the algorithm. In order to do so, we introduce the notion of the sharpness of a particular constraint set, which characterizes the difficulty of performing learning within the constraint set in an uncertain setting. This concept of sharpness allows us to identify the class of constraint sets for which the proposed algorithm is guaranteed to enjoy sublinear regret. Simulation results for this algorithm support the sublinear regret bound and provide empirical evidence that the sharpness of the constraint set impacts the performance of the algorithm.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 16 of its 28 references that are in the map. First posted on arXiv 1 May 2023.

Builds on

16 of 28 references.

References · 16

  1. 2016Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Roboticscited by 134
  2. 2018Learning-based Model Predictive Control for Safe Explorationcited by 120
  3. 2019Linear Stochastic Bandits Under Safety Constraintscited by 90
  4. 2018Stagewise Safe Bayesian Optimization with Gaussian Processescited by 79
  5. 2020Stochastic Bandits with Linear Constraintscited by 68
  6. 2016Conservative Contextual Linear Banditscited by 57
  7. 2019Safe Linear Thompson Sampling with Side Informationcited by 37
  8. 2015Safety-Constrained Reinforcement Learning for MDPscited by 33
  9. 2020Stage-wise Conservative Linear Banditscited by 28
  10. 2021Best Arm Identification with Safety Constraintscited by 25
  11. 2019Safe Convex Learning under Uncertain Constraintscited by 17
  12. 2021Safe Online Convex Optimization with Unknown Linear Safety Constraintscited by 13
4 more
  1. 2020Safe Learning under Uncertain Objectives and Constraintscited by 7
  2. 2017Correlational Dueling Bandits with Application to Clinical Treatment in Large Decision Spacescited by 6
  3. 2019Safe non-smooth black-box optimization with application to policy searchcited by 6
  4. 2022Robust Model Predictive Control of Time-Delay Systems through System Level Synthesiscited by 2

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Cited by year

Citing papers per year: 2023: 1; 2024: 0; 2025: 2.

3 papers.

  1. 2023Convex Methods for Constrained Linear Banditscited by 5
  2. 2025Constrained Linear Thompson Samplingcited by 0
  3. 2025The Safety-Privacy Tradeoff in Linear Banditscited by 0