Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
149 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Randomized Gaussian Process Upper Confidence Bound with Tighter Bayesian Regret Bounds (2302.01511v2)

Published 3 Feb 2023 in cs.LG

Abstract: Gaussian process upper confidence bound (GP-UCB) is a theoretically promising approach for black-box optimization; however, the confidence parameter $\beta$ 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 $\beta$. 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.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (43)
  1. Multi-fidelity high-throughput optimization of electrical conductivity in P3HT-CNT composites. Advanced Functional Materials, page 2102606, 2021.
  2. M. A. Beg. On the estimation of pr {Y<X}𝑌𝑋\{Y<X\}{ italic_Y < italic_X } for the two-parameter exponential distribution. Metrika, 27(1):29–34, 1980.
  3. Randomised Gaussian process upper confidence bound for Bayesian optimisation. In Proceedings of the 29th International Joint Conference on Artificial Intelligence, pages 2284–2290. International Joint Conferences on Artificial Intelligence Organization, 2020.
  4. Adversarially robust optimization with Gaussian processes. In Advances in Neural Information Processing Systems 31, pages 5760–5770. Curran Associates, Inc., 2018.
  5. A. D. Bull. Convergence rates of efficient global optimization algorithms. Journal of Machine Learning Research, 12(10), 2011.
  6. S. R. Chowdhury and A. Gopalan. On kernelized multi-armed bandits. In Proceedings of the 34th International Conference on Machine Learning, volume 70 of Proceedings of Machine Learning Research, pages 844–853, 2017.
  7. Parallel Gaussian process optimization with upper confidence bound and pure exploration. In Proceedings of the 2013th European Conference on Machine Learning and Knowledge Discovery in Databases, pages 225–240. Springer-Verlag, 2013.
  8. Parallelizing exploration-exploitation tradeoffs in Gaussian process bandit optimization. Journal of Machine Learning Research, 15:4053–4103, 2014.
  9. Constrained Bayesian optimization for automatic chemical design using variational autoencoders. Chemical science, 11(2):577–586, 2020.
  10. P. Hennig and C. J. Schuler. Entropy search for information-efficient global optimization. Journal of Machine Learning Research, 13(57):1809–1837, 2012.
  11. Predictive entropy search for efficient global optimization of black-box functions. In Advances in Neural Information Processing Systems 27, page 918–926. Curran Associates, Inc., 2014.
  12. Joint entropy search for maximally-informed Bayesian optimization. In Advances in Neural Information Processing Systems, 2022. To appear.
  13. Bayesian optimization for distributionally robust chance-constrained problem. In Proceedings of the 39th International Conference on Machine Learning, volume 162, pages 9602–9621. PMLR, 2022.
  14. Mean-variance analysis in Bayesian optimization under uncertainty. In Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, volume 130, pages 973–981. PMLR, 2021.
  15. Bandit optimisation of functions in the Matérn kernel RKHS. In Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics, volume 108 of Proceedings of Machine Learning Research, pages 2486–2495, 2020.
  16. High dimensional Bayesian optimisation and bandits via additive models. In Proceedings of the 32nd International Conference on Machine Learning, volume 37 of Proceedings of Machine Learning Research, pages 295–304, 2015.
  17. Gaussian process bandit optimisation with multi-fidelity evaluations. In Advances in Neural Information Processing Systems 29, pages 1000–1008. Curran Associates, Inc., 2016.
  18. Multi-fidelity Bayesian optimisation with continuous approximations. In Proceedings of the 34th International Conference on Machine Learning, volume 70 of Proceedings of Machine Learning Research, pages 1799–1808, 2017.
  19. Parallelised Bayesian optimisation via Thompson sampling. In Proceedings of the 21st International Conference on Artificial Intelligence and Statistics, volume 84 of Proceedings of Machine Learning Research, pages 133–142, 2018a.
  20. Neural architecture search with Bayesian optimisation and optimal transport. Advances in neural information processing systems 31, pages 2016–2025, 2018b.
  21. ChemBO: Bayesian optimization of small organic molecules with synthesizable recommendations. In Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics, volume 108 of Proceedings of Machine Learning Research, pages 3393–3403, 2020.
  22. Bayesian optimization for cascade-type multistage processes. Neural Computation, 34(12):2408–2431, 2022.
  23. Estimation of parameters in a two-parameter exponential distribution using ranked set sample. Annals of the Institute of Statistical Mathematics, 46(4):723–736, 1994.
  24. Benchmarking the performance of Bayesian optimization across multiple experimental materials science domains. npj Computational Material, 7(188), 2021.
  25. Two-step machine learning enables optimized nanoparticle synthesis. npj Computational Materials, 7(1):1–10, 2021.
  26. The application of Bayesian methods for seeking the extremum. Towards Global Optimization, 2(117-129):2, 1978.
  27. A flexible framework for multi-objective Bayesian optimization using random scalarizations. In Proceedings of The 35th Uncertainty in Artificial Intelligence Conference, volume 115 of Proceedings of Machine Learning Research, pages 766–776, 2020.
  28. A. Rahimi and B. Recht. Random features for large-scale kernel machines. In Advances in Neural Information Processing Systems 20, pages 1177–1184. Curran Associates, Inc., 2008.
  29. Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning). The MIT Press, 2005.
  30. D. Russo and B. Van Roy. Learning to optimize via posterior sampling. Mathematics of Operations Research, 39(4):1221–1243, 2014.
  31. Taking the human out of the loop: A review of Bayesian optimization. Proceedings of the IEEE, 104(1):148–175, 2016.
  32. Practical Bayesian optimization of machine learning algorithms. In Advances in Neural Information Processing Systems 25, pages 2951–2959. Curran Associates, Inc., 2012.
  33. Gaussian process optimization in the bandit setting: No regret and experimental design. In Proceedings of the 27th International Conference on Machine Learning, pages 1015–1022. Omnipress, 2010.
  34. A data fusion approach to optimize compositional stability of halide perovskites. Matter, 4(4):1305–1322, 2021.
  35. Multi-objective Bayesian optimization using Pareto-frontier entropy. In Proceedings of the 37th International Conference on Machine Learning, volume 119, pages 9279–9288. PMLR, 2020.
  36. Multi-fidelity Bayesian optimization with max-value entropy search and its parallelization. In Proceedings of the 37th International Conference on Machine Learning, volume 119, pages 9334–9345. PMLR, 2020.
  37. A Generalized Framework of Multifidelity Max-Value Entropy Search Through Joint Entropy. Neural Computation, 34(10):2145–2203, 2022a.
  38. Sequential and parallel constrained max-value entropy search via information lower bound. In Proceedings of the 39th International Conference on Machine Learning, volume 162 of Proceedings of Machine Learning Research, pages 20960–20986, 2022b.
  39. COMBO: An efficient Bayesian optimization library for materials science. Materials discovery, 4:18–21, 2016.
  40. On information gain and regret bounds in Gaussian process bandits. In Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, volume 130 of Proceedings of Machine Learning Research, pages 82–90, 2021.
  41. Z. Wang and S. Jegelka. Max-value entropy search for efficient Bayesian optimization. In Proceedings of the 34th International Conference on Machine Learning, volume 70 of Proceedings of Machine Learning Research, pages 3627–3635, 2017.
  42. Optimization as estimation with Gaussian processes in bandit settings. In Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, volume 51 of Proceedings of Machine Learning Research, pages 1022–1031, 2016.
  43. e-PAL: An active learning approach to the multi-objective optimization problem. Journal of Machine Learning Research, 17(104):1–32, 2016.
Citations (9)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now