mlsanityData to 7 Oct 2026

Robust Uncertainty Bounds in Reproducing Kernel Hilbert Spaces: A Convex Optimization Approach

arXiv 2104.09582 ↗First posted 19 Apr 2021cs.LG cs.SY eess.SYcited by 14

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Abstract (arXiv)

The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where outputs are corrupted by bounded measurement noise. The noise can originate from any compactly supported distribution and no independence assumptions are made on the available data. In this setting, we show how computing tight, finite-sample uncertainty bounds amounts to solving parametric quadratically constrained linear programs. Next, properties of our approach are established and its relationship with another methods is studied. Numerical experiments are presented to exemplify how the theory can be applied in a number of scenarios, and to contrast it with other closed-form alternatives.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Builds on 20 of its 53 references that are in the map. First posted on arXiv 19 Apr 2021.

Builds on

20 of 53 references.

References · 20

  1. 2017On Kernelized Multi-armed Banditscited by 348
  2. 2017Safe Model-based Reinforcement Learning with Stability Guaranteescited by 347
  3. 2018Gaussian Process Behaviour in Wide Deep Neural Networkscited by 314
  4. 2019Causality for Machine Learningcited by 242
  5. 2018Gaussian Processes and Kernel Methods: A Review on Connections and Equivalencescited by 188
  6. 2019Mean-field theory of two-layers neural networks: dimension-free bounds and kernel limitcited by 187
  7. 2018Learning-based Model Predictive Control for Safe Explorationcited by 116
  8. 2017Cautious Model Predictive Control using Gaussian Process Regressioncited by 91
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  12. 2020Every Model Learned by Gradient Descent Is Approximately a Kernel Machinecited by 53
8 more
  1. 2016Learning Model Predictive Control for iterative tasks. A Data-Driven Control Frameworkcited by 38
  2. 2018Approximation beats concentration? An approximation view on inference with smooth radial kernelscited by 33
  3. 2020Planning with Learned Dynamics: Probabilistic Guarantees on Safety and Reachability via Lipschitz Constantscited by 25
  4. 2019Feedback Linearization based on Gaussian Processes with event-triggered Online Learningcited by 24
  5. 2020Deterministic error bounds for kernel-based learning techniques under bounded noisecited by 24
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 3; 2025: 5; 2026: 3.

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  1. 2023Koopman Kernel Regressioncited by 22
  2. 2023Automatic nonlinear MPC approximation with closed-loop guaranteescited by 12
  3. 2025Safe exploration in reproducing kernel Hilbert spacescited by 10
  4. 2024PACSBO: Probably approximately correct safe Bayesian optimizationcited by 8
  5. 2024Tighter Confidence Bounds for Sequential Kernel Regressioncited by 7
  6. 2025Optimal kernel regression bounds under energy-bounded noisecited by 4
  7. 2025Streaming Generated Gaussian Process Experts for Online Learning and Control: Extended Versioncited by 4
  8. 2024Safe reinforcement learning in uncertain contextscited by 1
  9. 2025Derandomizing Simultaneous Confidence Regions for Band-Limited Functions by Improved Norm Bounds and Majority-Voting Schemescited by 1
  10. 2025Single Image Inpainting and Super-Resolution with Simultaneous Uncertainty Guarantees by Universal Reproducing Kernelscited by 1
  11. 2026Optimal uncertainty bounds for multivariate kernel regression under bounded noise: A Gaussian process-based dual functioncited by 1
  12. 2023Episodic Gaussian Process-Based Learning Control with Vanishing Tracking Errorscited by 0
2 more
  1. 2026On Uniform Error Bounds for Kernel Regression under Non-Gaussian Noisecited by 0
  2. 2026Mitigating Over-Optimization in PRM-Guided Search in Mathematical Reasoning by Optimizing the Guidecited by 0