Advanced Monte Carlo for Acquisition Sampling in Bayesian Optimization
Optimizing complex systems usually involves costly and time-consuming experiments, where selecting the experiments to perform is fundamental. Bayesian optimization (BO) has proved to be a suitable optimization method in these situations thanks to its sample efficiency and principled way of learning...
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MDPI AG
2025-01-01
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| Online Access: | https://www.mdpi.com/1099-4300/27/1/58 |
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| author | Javier Garcia-Barcos Ruben Martinez-Cantin |
| author_facet | Javier Garcia-Barcos Ruben Martinez-Cantin |
| author_sort | Javier Garcia-Barcos |
| collection | DOAJ |
| description | Optimizing complex systems usually involves costly and time-consuming experiments, where selecting the experiments to perform is fundamental. Bayesian optimization (BO) has proved to be a suitable optimization method in these situations thanks to its sample efficiency and principled way of learning from previous data, but it typically requires that experiments are sequentially performed. Fully distributed BO addresses the need for efficient parallel and asynchronous active search, especially where traditional centralized BO faces limitations concerning privacy in federated learning and resource utilization in high-performance computing settings. Boltzmann sampling is an embarrassingly parallel method that enables fully distributed BO using Monte Carlo sampling. However, it also requires sampling from a continuous acquisition function, which can be challenging even for advanced Monte Carlo methods due to its highly multimodal nature, constrained search space, and possibly numerically unstable values. We introduce a simplified version of Boltzmann sampling, and we analyze multiple Markov chain Monte Carlo (MCMC) methods with a numerically improved log EI implementation for acquisition sampling. Our experiments suggest that by introducing gradient information during MCMC sampling, methods such as the MALA or CyclicalSGLD improve acquisition sampling efficiency. Interestingly, a mixture of proposals for the Metropolis–Hastings approach proves to be effective despite its simplicity. |
| format | Article |
| id | doaj-art-365eafbf569f4121a669756b970c84a8 |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-365eafbf569f4121a669756b970c84a82025-01-24T13:31:51ZengMDPI AGEntropy1099-43002025-01-012715810.3390/e27010058Advanced Monte Carlo for Acquisition Sampling in Bayesian OptimizationJavier Garcia-Barcos0Ruben Martinez-Cantin1Instituto Universitario de Investigacion en Ingenieria de Aragon (I3A), Universidad de Zaragoza, 50018 Zaragoza, SpainInstituto Universitario de Investigacion en Ingenieria de Aragon (I3A), Universidad de Zaragoza, 50018 Zaragoza, SpainOptimizing complex systems usually involves costly and time-consuming experiments, where selecting the experiments to perform is fundamental. Bayesian optimization (BO) has proved to be a suitable optimization method in these situations thanks to its sample efficiency and principled way of learning from previous data, but it typically requires that experiments are sequentially performed. Fully distributed BO addresses the need for efficient parallel and asynchronous active search, especially where traditional centralized BO faces limitations concerning privacy in federated learning and resource utilization in high-performance computing settings. Boltzmann sampling is an embarrassingly parallel method that enables fully distributed BO using Monte Carlo sampling. However, it also requires sampling from a continuous acquisition function, which can be challenging even for advanced Monte Carlo methods due to its highly multimodal nature, constrained search space, and possibly numerically unstable values. We introduce a simplified version of Boltzmann sampling, and we analyze multiple Markov chain Monte Carlo (MCMC) methods with a numerically improved log EI implementation for acquisition sampling. Our experiments suggest that by introducing gradient information during MCMC sampling, methods such as the MALA or CyclicalSGLD improve acquisition sampling efficiency. Interestingly, a mixture of proposals for the Metropolis–Hastings approach proves to be effective despite its simplicity.https://www.mdpi.com/1099-4300/27/1/58Bayesian optimizationGaussian processMCMC |
| spellingShingle | Javier Garcia-Barcos Ruben Martinez-Cantin Advanced Monte Carlo for Acquisition Sampling in Bayesian Optimization Entropy Bayesian optimization Gaussian process MCMC |
| title | Advanced Monte Carlo for Acquisition Sampling in Bayesian Optimization |
| title_full | Advanced Monte Carlo for Acquisition Sampling in Bayesian Optimization |
| title_fullStr | Advanced Monte Carlo for Acquisition Sampling in Bayesian Optimization |
| title_full_unstemmed | Advanced Monte Carlo for Acquisition Sampling in Bayesian Optimization |
| title_short | Advanced Monte Carlo for Acquisition Sampling in Bayesian Optimization |
| title_sort | advanced monte carlo for acquisition sampling in bayesian optimization |
| topic | Bayesian optimization Gaussian process MCMC |
| url | https://www.mdpi.com/1099-4300/27/1/58 |
| work_keys_str_mv | AT javiergarciabarcos advancedmontecarloforacquisitionsamplinginbayesianoptimization AT rubenmartinezcantin advancedmontecarloforacquisitionsamplinginbayesianoptimization |