[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125224-en":3,"doc-seo-125224-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},125224,1099514067438,"River Wang","https://ap-avatar.wpscdn.com/avatar/100002539ee87300030?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780474512215547542",8,"Research & Report","Discrete Bayesian Optimization via Machine Learning - Preprint","Bayesian Optimization (BO) addresses expensive black-box optimization by iteratively updating a surrogate model and balancing exploration with exploitation to reach near-optimal solutions in few evaluations. Adaptations for discrete, constrained settings are motivated by applications such as cloud computing, where configuration search must satisfy Quality of Service constraints while minimizing provider and user costs. This work presents d-MALIBOO, a BO-driven method enhanced with machine learning to model feasible constraint regions and guide search in discrete bounded domains, incorporating an ε-greedy strategy for exploration in multi-modal landscapes. Experimental results show significant regret reductions versus OpenTuner and SVM-CBO.","Discrete Bayesian Optimization via Machine Learning  \nRoberto Salaa,, Bruno Guindania , Danilo Ardagnaa , Alessandra Guglielmia ,  \na Politecnico di Milano, Piazza Leonardo da Vinci, 32, Milano, 20133, Italy  \n[name.surname@polimi.it](name.surname@polimi.it)  \nAbstract  \nBayesian Optimization (BO) is a family of powerful algorithms designed to solve complex optimization problems involving expensive black-box functions. These sequential algorithms iteratively update a surrogate model of the objective function (OF), effectively balancing exploration and exploitation to identify near-optimal solutions within a limited number of iterations. Originally designed for continuous, unconstrained domains, its efficiency has inspired adaptations for discrete, constrained optimization problems. On the other hand, Machine Learning (ML) models allow accurate predictions for black-box functions, although they typically require large amounts of data for training. Leveraging the strengths of BO and ML, research tackles the challenge of identifying optimal configurations in the context of cloud computing. This paradigm has become pervasive due to its ability to provide flexible and scalable resources. Identifying the optimal hardware-software configuration is essential for minimizing costs while meeting Quality of Service constraints. This task involves solving complex optimization problems over multidimensional discrete domains and black-box objective functions and constraints, within a limited number of iterations. To address this challenge, this work introduces d-MALIBOO, a BO-based algorithm that integrates ML techniques to enhance the efficiency of finding near-optimal solutions in discrete and bounded domains. While BO builds the surrogate model of the OF, ML models determine the feasible region of the black-box constraints and guide the BO algorithm toward promising regions of the discrete domain. Furthermore, we introduce an ε-greedy approach to favor exploration in domains with multiple local optima. Experimental results show that our algorithm outperforms OpenTuner, a popular framework for constrained optimization, by reducing the average regret by 29%, and SVM-CBO, a BO-based algorithm that integrates SVM models to determine the feasible region, by 82% .  \nPreprint submitted to Performance Evaluation January 16, 2025  \nKeywords: Discrete Variables, Bayesian Optimization, Machine Learning, Black-box Optimization, Cloud Computing  \n1. Introduction  \nThe Cloud computing paradigm has become pervasive across various domains, including industry, e-commerce, blockchain technology, and drug discovery [1, 2, 3, 4] . Among these, it plays a fundamental role in the development of Artificial Intelligence (AI) and Large Language Models [5, 6] . Cloud computing offers flexible and scalable resources, leveraging a vast pool of virtually unlimited Virtual Machines (VMs) housed in data centers. The diverse range of use cases and the heterogeneous nature of machines within these data centers make it essential to identify optimal configurations for both applications and infrastructure. Inefficient configurations can lead to substantial costs for providers and users alike [7] . Moreover, these applications often require Quality of Service (QoS) criteria to be met, such as achieving a maximum model accuracy or maintaining a minimum pipeline response time. This requirement translates into constrained optimization problems over discrete, multidimensional domains. In the aforementioned scenarios, frequently each application run incurs a high cost, either in terms of time or money. Consequently, the optimization process must be carried out in a limited number of iterations. Consider, for example, determining the optimal hardware-software configuration for an AI application. The goal is to maximize the model accuracy (at training time) guaranteeing low response time and costs (at inference time when the AI model is in production) . In such cases, each configur","cbCaid4V6V5R8kI0","https://ap.wps.com/l/cbCaid4V6V5R8kI0","pdf",1998091,1,32,"English","en",105,"# Introduction\n## Problem Setting: Cloud Configuration as Constrained Discrete Optimization\n## Core Methods: Bayesian Optimization and Surrogate Modeling\n## Proposed Contribution: d-MALIBOO for Discrete Constrained Domains\n## Exploration Strategy: ε-greedy in Multi-Local Optima Domains","[{\"question\":\"What makes cloud configuration a discrete constrained optimization problem?\",\"answer\":\"Cloud deployments require selecting hardware-software configurations across heterogeneous machines, under Quality of Service constraints. The search space is discrete and multidimensional, and each evaluation can be costly in time or money, so only a limited number of iterations is feasible.\"},{\"question\":\"How does Bayesian Optimization work for expensive black-box functions?\",\"answer\":\"BO iteratively updates a surrogate model of the objective function and chooses the next evaluation point by trading off exploration of uncertainty with exploitation of promising objective values. This enables convergence toward near-optimal solutions using few evaluations.\"},{\"question\":\"What is d-MALIBOO and how does it combine BO with machine learning?\",\"answer\":\"d-MALIBOO is a BO-based algorithm for constrained optimization in discrete bounded domains. It uses machine learning models to estimate the feasible region from black-box constraints, guiding BO toward promising regions, and adds an ε-greedy strategy to encourage exploration when multiple local optima exist.\"}]","Discrete Bayesian Optimization via Machine Learning - Preprint | PDF",1785897587,81,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"discrete-bayesian-optimization-via-machine-learning-preprint","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/discrete-bayesian-optimization-via-machine-learning-preprint/125224/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What makes cloud configuration a discrete constrained optimization problem?","Question",{"text":75,"@type":76},"Cloud deployments require selecting hardware-software configurations across heterogeneous machines, under Quality of Service constraints. The search space is discrete and multidimensional, and each evaluation can be costly in time or money, so only a limited number of iterations is feasible.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does Bayesian Optimization work for expensive black-box functions?",{"text":80,"@type":76},"BO iteratively updates a surrogate model of the objective function and chooses the next evaluation point by trading off exploration of uncertainty with exploitation of promising objective values. This enables convergence toward near-optimal solutions using few evaluations.",{"name":82,"@type":73,"acceptedAnswer":83},"What is d-MALIBOO and how does it combine BO with machine learning?",{"text":84,"@type":76},"d-MALIBOO is a BO-based algorithm for constrained optimization in discrete bounded domains. It uses machine learning models to estimate the feasible region from black-box constraints, guiding BO toward promising regions, and adds an ε-greedy strategy to encourage exploration when multiple local optima exist.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]