mlsanityData to 7 Oct 2026

Randomized Gaussian Process Upper Confidence Bound with Tighter Bayesian Regret Bounds

arXiv 2302.01511 ↗First posted 3 Feb 2023cs.LGcited by 16

Not on the map. Why?

Abstract (arXiv)

Gaussian process upper confidence bound (GP-UCB) is a theoretically promising approach for black-box optimization; however, the confidence parameter β is considerably large in the theorem and chosen heuristically in practice. Then, randomized GP-UCB (RGP-UCB) uses a randomized confidence parameter, which follows the Gamma distribution, to mitigate the impact of manually specifying β. This study first generalizes the regret analysis of RGP-UCB to a wider class of distributions, including the Gamma distribution. Furthermore, we propose improved RGP-UCB (IRGP-UCB) based on a two-parameter exponential distribution, which achieves tighter Bayesian regret bounds. IRGP-UCB does not require an increase in the confidence parameter in terms of the number of iterations, which avoids over-exploration in the later iterations. Finally, we demonstrate the effectiveness of IRGP-UCB through extensive experiments.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 22 of its 45 references that are in the map. First posted on arXiv 3 Feb 2023.

Builds on

22 of 45 references.

References · 22

  1. 2017On Kernelized Multi-armed Banditscited by 348
  2. 2013Learning to Optimize Via Posterior Samplingcited by 253
  3. 2017Max-value Entropy Search for Efficient Bayesian Optimizationcited by 202
  4. 2014Predictive Entropy Search for Efficient Global Optimization of Black-box Functionscited by 201
  5. 2018Neural Architecture Search with Bayesian Optimisation and Optimal Transportcited by 192
  6. 2020On Information Gain and Regret Bounds in Gaussian Process Banditscited by 156
  7. 2015High Dimensional Bayesian Optimisation and Bandits via Additive Modelscited by 137
  8. 2017Multi-fidelity Bayesian Optimisation with Continuous Approximationscited by 120
  9. 2018A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizationscited by 98
  10. 2019ChemBO: Bayesian Optimization of Small Organic Molecules with Synthesizable Recommendationscited by 77
  11. 2018Adversarially Robust Optimization with Gaussian Processescited by 61
  12. 2019Multi-objective Bayesian Optimization using Pareto-frontier Entropycited by 57
10 more
  1. 2022Joint Entropy Search for Maximally-Informed Bayesian Optimizationcited by 55
  2. 2013Parallel Gaussian Process Optimization with Upper Confidence Bound and Pure Explorationcited by 50
  3. 2021Benchmarking the Performance of Bayesian Optimization across Multiple Experimental Materials Science Domainscited by 46
  4. 2020Bandit optimisation of functions in the Mat'ern kernel RKHScited by 40
  5. 2021Sequential- and Parallel- Constrained Max-value Entropy Search via Information Lower Boundcited by 23
  6. 2020Randomised Gaussian Process Upper Confidence Bound for Bayesian Optimisationcited by 22
  7. 2020Mean-Variance Analysis in Bayesian Optimization under Uncertaintycited by 18
  8. 2015Optimization as Estimation with Gaussian Processes in Bandit Settingscited by 17
  9. 2021Bayesian Optimization for Cascade-type Multi-stage Processescited by 17
  10. 2022Bayesian Optimization for Distributionally Robust Chance-constrained Problemcited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 4; 2024: 3; 2025: 4; 2026: 5.

16 papers.

Sort:

  1. 2023Looping in the Human Collaborative and Explainable Bayesian Optimizationcited by 27
  2. 2023Self-Correcting Bayesian Optimization through Bayesian Active Learningcited by 22
  3. 2023Posterior Sampling-Based Bayesian Optimization with Tighter Bayesian Regret Boundscited by 15
  4. 2025Improved Regret Bounds for Gaussian Process Upper Confidence Bound in Bayesian Optimizationcited by 13
  5. 2025Improved Regret Analysis in Gaussian Process Bandits: Optimality for Noiseless Reward, RKHS norm, and Non-Stationary Variancecited by 12
  6. 2024Regret Analysis for Randomized Gaussian Process Upper Confidence Boundcited by 4
  7. 2024Active Learning for Level Set Estimation Using Randomized Straddle Algorithmscited by 3
  8. 2025Distributionally Robust Active Learning for Gaussian Process Regressioncited by 3
  9. 2025Regret Analysis of Posterior Sampling-Based Expected Improvement for Bayesian Optimizationcited by 3
  10. 2023Bayesian Analysis of Combinatorial Gaussian Process Banditscited by 2
  11. 2026Randomized Kriging Believer for Parallel Bayesian Optimization with Regret Boundscited by 2
  12. 2026Posterior Sampling Reinforcement Learning with Gaussian Processes for Continuous Control: Sublinear Regret Bounds for Unbounded State Spacescited by 2
4 more
  1. 2026On Regret Bounds of Thompson Sampling for Bayesian Optimizationcited by 2
  2. 2024Optimal Policy Learning with Observational Data in Multi-Action Scenarios: Estimation, Risk Preference, and Potential Failurescited by 1
  3. 2026Nearly-Optimal Algorithm for Adversarial Kernelized Banditscited by 1
  4. 2026Towards Regret Guarantees for One-Step Lookahead Bayesian Optimizationcited by 0