Energy Efficient Hyperparameter Optimisation (e2HPO) for classification and regression tasks

Energy Efficient Hyperparameter Optimisation (e2HPO) for classification and regression tasks | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Energy Efficient Hyperparameter Optimisation (e 2 HPO) for classification and regression tasks Antonio Candelieri, Elena Signori, Francesca Reina This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8520706/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 9 You are reading this latest preprint version Abstract Although it is well-established that Artificial Intelligence can enable and support sustainability in many application domains, its own sustainability is a critical challenge for research and industry. The need for more accurate Machine Learning models clashes with the fact that a linear reduction in the generalisation error requires exponentially larger resources: a more complex model, more training data and experiments, and consequently more computational resources, entailing a higher energy consumption.This paper analyses an energy efficient hyperparameter optimisation algorithm, namely e$^2$HPO, on both classification and regression tasks. The approach integrates, into a unique framework, cost-aware and multiple information source Bayesian optimisation. Experiments on three common Machine Learning algorithms and five classification and four regression tasks empirically prove the benefits of the proposed algorithm against common hyperperameter optimisation based on vanilla Bayesian Optimisation. Despite this fully satisfactory general result, it turned out that some pair \textit{Machine Learning algorithm - dataset} can exhibit an intrinsic (non-linear) correlation between energy consumption and generalisation error; in this cases e$^2$HPO could slightly underperform against vanilla Bayesian Optimisation. GreenAutoML hyperparameter optimisation multiple information source Bayesian optimisation cost-aware Bayesian optimisation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 09 May, 2026 Reviews received at journal 23 Apr, 2026 Reviews received at journal 17 Apr, 2026 Reviewers agreed at journal 14 Apr, 2026 Reviewers agreed at journal 30 Mar, 2026 Reviewers invited by journal 11 Feb, 2026 Editor assigned by journal 08 Jan, 2026 Submission checks completed at journal 08 Jan, 2026 First submitted to journal 05 Jan, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8520706","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":590859910,"identity":"7c07a0d9-8bc0-41a2-8734-e0462eaa2767","order_by":0,"name":"Antonio Candelieri","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABDUlEQVRIie3Pv2vCQBTA8ZMH6fLKrQ8i8V944cA0VOi/ogScpGTs1CodshRcD/p/OCtZ2/0gHRShk4NT6ZChF/zRDqd0dLjvkByPfHgXIXy+i413LxI5CQEwbybIojV2fw5/CTck6B/IxG3g90g7i3xY7VwjX6eLdZ73hCzeF2bLN1FS4FeY57N2IqBYOgh9lKA0DwW93WepZlLt8noWaq4wHZ+4mMmCELm01xh17YEGGixBS3juJp0jkZtuWDM9acDPs4SPhOwW++wTYHCWxCZTCnmIZDYqfWGKNQTqtiHpc2uiHSQyg9Ua614kp6PYfD88dkiWqwrr6i65KpZb1+/vQ8cMHDOfz+fz/asfThJTdnXz9ZQAAAAASUVORK5CYII=","orcid":"","institution":"University of Milano-Bicocca","correspondingAuthor":true,"prefix":"","firstName":"Antonio","middleName":"","lastName":"Candelieri","suffix":""},{"id":590859911,"identity":"76bd0181-f090-4160-8d93-27f78379abbb","order_by":1,"name":"Elena Signori","email":"","orcid":"","institution":"Exacon s.r.l.","correspondingAuthor":false,"prefix":"","firstName":"Elena","middleName":"","lastName":"Signori","suffix":""},{"id":590859912,"identity":"754d4c74-be82-46e7-bf40-c4bd595ec56d","order_by":2,"name":"Francesca Reina","email":"","orcid":"","institution":"University of Milano-Bicocca","correspondingAuthor":false,"prefix":"","firstName":"Francesca","middleName":"","lastName":"Reina","suffix":""}],"badges":[],"createdAt":"2026-01-05 11:23:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8520706/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8520706/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102963119,"identity":"01180754-82c8-4202-9874-ab9a1bddebbe","added_by":"auto","created_at":"2026-02-19 04:13:37","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1001787,"visible":true,"origin":"","legend":"","description":"","filename":"CandelierietalSILION19.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8520706/v1_covered_30d5d8b4-0eb9-426d-a4d5-f209084853a1.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eEnergy Efficient Hyperparameter Optimisation (e\u003csup\u003e2\u003c/sup\u003eHPO) for classification and regression tasks\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"annals-of-mathematics-and-artificial-intelligence","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"amai","sideBox":"Learn more about [Annals of Mathematics and Artificial Intelligence](https://www.springer.com/journal/10472)","snPcode":"10472","submissionUrl":"https://submission.springernature.com/new-submission/10472/3","title":"Annals of Mathematics and Artificial Intelligence","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":" GreenAutoML, hyperparameter optimisation, multiple information source Bayesian optimisation, cost-aware Bayesian optimisation","lastPublishedDoi":"10.21203/rs.3.rs-8520706/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8520706/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Although it is well-established that Artificial Intelligence can enable and support sustainability in many application domains, its own sustainability is a critical challenge for research and industry. 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