mlsanityData to 7 Oct 2026

Bandit optimisation of functions in the Mat'ern kernel RKHS

arXiv 2001.10396 ↗First posted 28 Jan 2020cs.LG stat.MLcited by 40

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Abstract (arXiv)

We consider the problem of optimising functions in the reproducing kernel Hilbert space (RKHS) of a Mat'ern kernel with smoothness parameter nu over the domain [0,1]d under noisy bandit feedback. Our contribution, the π-GP-UCB algorithm, is the first practical approach with guaranteed sublinear regret for all nu>1 and d ≥ 1. Empirical validation suggests better performance and drastically improved computational scalablity compared with its predecessor, Improved GP-UCB.

Key facts. Cited by 40 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 Jan 2020.

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Citing papers per year: 2021: 8; 2022: 5; 2023: 11; 2024: 4; 2025: 5; 2026: 7.

40 papers.

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  1. 2021Gaussian Process Bandit Optimization with Few Batchescited by 57
  2. 2021Optimal Order Simple Regret for Gaussian Process Banditscited by 52
  3. 2021Neural Contextual Bandits without Regretcited by 40
  4. 2021Mitigating Covariate Shift in Imitation Learning via Offline Data Without Great Coveragecited by 26
  5. 2023On the Sublinear Regret of GP-UCBcited by 25
  6. 2023Kernelized Reinforcement Learning with Order Optimal Regret Boundscited by 20
  7. 2022Improved Convergence Rates for Sparse Approximation Methods in Kernel-Based Learningcited by 18
  8. 2023Randomized Gaussian Process Upper Confidence Bound with Tighter Bayesian Regret Boundscited by 16
  9. 2023Posterior Sampling-Based Bayesian Optimization with Tighter Bayesian Regret Boundscited by 15
  10. 2021Open Problem: Tight Online Confidence Intervals for RKHS Elementscited by 13
  11. 2025Improved Regret Bounds for Gaussian Process Upper Confidence Bound in Bayesian Optimizationcited by 13
  12. 2021Lenient Regret and Good-Action Identification in Gaussian Process Banditscited by 12
28 more
  1. 2025Improved Regret Analysis in Gaussian Process Bandits: Optimality for Noiseless Reward, RKHS norm, and Non-Stationary Variancecited by 12
  2. 2022A Robust Phased Elimination Algorithm for Corruption-Tolerant Gaussian Process Banditscited by 11
  3. 2024Tighter Confidence Bounds for Sequential Kernel Regressioncited by 7
  4. 2022Instance-Dependent Regret Analysis of Kernelized Banditscited by 5
  5. 2023Adaptation to Misspecified Kernel Regularity in Kernelised Banditscited by 5
  6. 2024Regret Analysis for Randomized Gaussian Process Upper Confidence Boundcited by 4
  7. 2024Sample-efficient Bayesian Optimisation Using Known Invariancescited by 4
  8. 2024Local Linearity: the Key for No-regret Reinforcement Learning in Continuous MDPscited by 4
  9. 2021Bayesian Optimistic Optimisation with Exponentially Decaying Regretcited by 3
  10. 2022On Average-Case Error Bounds for Kernel-Based Bayesian Quadraturecited by 3
  11. 2023(Private) Kernelized Bandits with Distributed Biased Feedbackcited by 3
  12. 2023On the Suboptimality of GP-UCB under Polynomial Effective Optimismcited by 3
  13. 2025Regret Analysis of Posterior Sampling-Based Expected Improvement for Bayesian Optimizationcited by 3
  14. 2026On Regret Bounds of Thompson Sampling for Bayesian Optimizationcited by 2
  15. 2026Batched Kernelized Bandits: Refinements and Extensionscited by 2
  16. 2021High-Dimensional Simulation Optimization via Brownian Fields and Sparse Gridscited by 0
  17. 2022Dual Instrumental Method for Confounded Kernelized Banditscited by 0
  18. 2023Reward Learning as Doubly Nonparametric Bandits: Optimal Design and Scaling Lawscited by 0
  19. 2023Physics Inspired Approaches To Understanding Gaussian Processescited by 0
  20. 2023Kernel ε-Greedy for Multi-Armed Bandits with Covariatescited by 0
  21. 2023Distributed Optimization via Kernelized Multi-armed Banditscited by 0
  22. 2025Linear Bandits beyond Inner Product Spaces, the case of Bandit Optimal Transportcited by 0
  23. 2025Safely Learning Controlled Stochastic Dynamicscited by 0
  24. 2026Sharper Guarantees for Misspecified Kernelized Bandit Optimizationcited by 0
  25. 2026Learning Kernel-Based MDPs from Episodic Preferential Feedbackcited by 0
  26. 2026Near-Optimal Regret in Adversarial Kernel Banditscited by 0
  27. 2026UBP2: Uncertainty-Balanced Preference Planning for Efficient Preference-based Reinforcement Learningcited by 0
  28. 2026Improved Regret Analysis for Parallel Gaussian Process Bandit Optimizationcited by 0