{"title":"基于局部在线保形预测的鲁棒贝叶斯优化","authors":"Dongwon Kim;Matteo Zecchin;Sangwoo Park;Joonhyuk Kang;Osvaldo Simeone","doi":"10.1109/TSP.2025.3559568","DOIUrl":null,"url":null,"abstract":"Bayesian optimization (BO) is a sequential approach for optimizing black-box objective functions using zeroth-order noisy observations. In BO, Gaussian processes (GPs) are employed as probabilistic surrogate models to estimate the objective function based on past observations, guiding the selection of future queries to maximize utility. However, the performance of BO heavily relies on the quality of these probabilistic estimates, which can deteriorate significantly under model misspecification. To address this issue, we introduce localized online conformal prediction-based Bayesian optimization (LOCBO), a BO algorithm that calibrates the GP model through localized online conformal prediction (CP). LOCBO corrects the GP likelihood based on predictive sets produced by LOCBO, and the corrected GP likelihood is then denoised to obtain a calibrated posterior distribution on the objective function. The likelihood calibration step leverages an input-dependent calibration threshold to tailor coverage guarantees to different regions of the input space. Under minimal noise assumptions, we provide theoretical performance guarantees for LOCBO’s iterates that hold for the unobserved objective function. These theoretical findings are validated through experiments on synthetic and real-world optimization tasks, demonstrating that LOCBO consistently outperforms state-of-the-art BO algorithms in the presence of model misspecification.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"2039-2052"},"PeriodicalIF":4.6000,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Robust Bayesian Optimization via Localized Online Conformal Prediction\",\"authors\":\"Dongwon Kim;Matteo Zecchin;Sangwoo Park;Joonhyuk Kang;Osvaldo Simeone\",\"doi\":\"10.1109/TSP.2025.3559568\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Bayesian optimization (BO) is a sequential approach for optimizing black-box objective functions using zeroth-order noisy observations. In BO, Gaussian processes (GPs) are employed as probabilistic surrogate models to estimate the objective function based on past observations, guiding the selection of future queries to maximize utility. However, the performance of BO heavily relies on the quality of these probabilistic estimates, which can deteriorate significantly under model misspecification. To address this issue, we introduce localized online conformal prediction-based Bayesian optimization (LOCBO), a BO algorithm that calibrates the GP model through localized online conformal prediction (CP). LOCBO corrects the GP likelihood based on predictive sets produced by LOCBO, and the corrected GP likelihood is then denoised to obtain a calibrated posterior distribution on the objective function. The likelihood calibration step leverages an input-dependent calibration threshold to tailor coverage guarantees to different regions of the input space. Under minimal noise assumptions, we provide theoretical performance guarantees for LOCBO’s iterates that hold for the unobserved objective function. These theoretical findings are validated through experiments on synthetic and real-world optimization tasks, demonstrating that LOCBO consistently outperforms state-of-the-art BO algorithms in the presence of model misspecification.\",\"PeriodicalId\":13330,\"journal\":{\"name\":\"IEEE Transactions on Signal Processing\",\"volume\":\"73 \",\"pages\":\"2039-2052\"},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2025-04-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE Transactions on Signal Processing\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/10964108/\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Signal Processing","FirstCategoryId":"5","ListUrlMain":"https://ieeexplore.ieee.org/document/10964108/","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
Robust Bayesian Optimization via Localized Online Conformal Prediction
Bayesian optimization (BO) is a sequential approach for optimizing black-box objective functions using zeroth-order noisy observations. In BO, Gaussian processes (GPs) are employed as probabilistic surrogate models to estimate the objective function based on past observations, guiding the selection of future queries to maximize utility. However, the performance of BO heavily relies on the quality of these probabilistic estimates, which can deteriorate significantly under model misspecification. To address this issue, we introduce localized online conformal prediction-based Bayesian optimization (LOCBO), a BO algorithm that calibrates the GP model through localized online conformal prediction (CP). LOCBO corrects the GP likelihood based on predictive sets produced by LOCBO, and the corrected GP likelihood is then denoised to obtain a calibrated posterior distribution on the objective function. The likelihood calibration step leverages an input-dependent calibration threshold to tailor coverage guarantees to different regions of the input space. Under minimal noise assumptions, we provide theoretical performance guarantees for LOCBO’s iterates that hold for the unobserved objective function. These theoretical findings are validated through experiments on synthetic and real-world optimization tasks, demonstrating that LOCBO consistently outperforms state-of-the-art BO algorithms in the presence of model misspecification.
期刊介绍:
The IEEE Transactions on Signal Processing covers novel theory, algorithms, performance analyses and applications of techniques for the processing, understanding, learning, retrieval, mining, and extraction of information from signals. The term “signal” includes, among others, audio, video, speech, image, communication, geophysical, sonar, radar, medical and musical signals. Examples of topics of interest include, but are not limited to, information processing and the theory and application of filtering, coding, transmitting, estimating, detecting, analyzing, recognizing, synthesizing, recording, and reproducing signals.