Q-CMAPO: A quantum-classical framework for balancing exploration and exploitation in multi-agent reinforcement learning

Q-CMAPO: A quantum-classical framework for balancing exploration and exploitation in multi-agent reinforcement learning | 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 Q-CMAPO: A quantum-classical framework for balancing exploration and exploitation in multi-agent reinforcement learning Mazyar Taghavi, Javad Vahidi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7111581/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 03 Feb, 2026 Read the published version in Quantum Machine Intelligence → Version 1 posted 6 You are reading this latest preprint version Abstract In this paper, we propose a novel approach, Q-CMAPO (Quantum-Classical Multi-agent Policy Optimization), for tackling complex decision-making problems in multi-agent systems. By leveraging quantum-inspired optimization techniques, Q-CMAPO efficiently addresses the exploration-exploitation tradeoff, enhancing the scalability and performance of reinforcement learning (RL) algorithms in partially observable, non-stationary environments. We introduce an innovative framework that combines centralized training with decentralized execution (CTDE), enabling seamless cooperation between agents while preserving their autonomy during execution. Through extensive empirical evaluation, including various UAV deployment scenarios, we demonstrate that Q-CMAPO consistently outperforms existing baselines in both computational efficiency and classification accuracy. Our experiments show significant improvements in performance metrics, as well as substantial gains in runtime efficiency and memory utilization. Furthermore, we provide a comprehensive theoretical analysis, proving the convergence and stability of the proposed method in non-stationary environments. We also conduct an ablation study, shedding light on the importance of different components of Q-CMAPO in optimizing agent cooperation. While promising, the proposed approach faces several challenges, including its sensitivity to hyperparameters and scalability in large-scale systems, suggesting opportunities for future refinement and expansion. The integration of Q-CMAPO into real-world applications, such as autonomous robotics, and UAV-based surveillance, opens new avenues for research, bridging the gap between quantum-inspired optimization and practical deployment in multi-agent systems. Quantum optimization Multi-agent reinforcement learning Exploration exploitation Unmanned aerial vehicle Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 03 Feb, 2026 Read the published version in Quantum Machine Intelligence → Version 1 posted Reviewers agreed at journal 28 Jul, 2025 Reviewers agreed at journal 27 Jul, 2025 Reviewers invited by journal 27 Jul, 2025 Editor assigned by journal 22 Jul, 2025 Submission checks completed at journal 15 Jul, 2025 First submitted to journal 13 Jul, 2025 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-7111581","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":491774303,"identity":"5c05fa13-26ab-48a9-9de1-8a89985169f7","order_by":0,"name":"Mazyar Taghavi","email":"data:image/png;base64,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","orcid":"","institution":"Iran University of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Mazyar","middleName":"","lastName":"Taghavi","suffix":""},{"id":491774304,"identity":"17e44796-c7f1-49a8-8e47-ee38388d25ec","order_by":1,"name":"Javad Vahidi","email":"","orcid":"","institution":"Iran University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Javad","middleName":"","lastName":"Vahidi","suffix":""}],"badges":[],"createdAt":"2025-07-13 06:38:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7111581/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7111581/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s42484-026-00361-0","type":"published","date":"2026-02-03T15:57:51+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":102235597,"identity":"986c4afe-6c5b-4aba-b944-498defb29121","added_by":"auto","created_at":"2026-02-09 16:17:10","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3723920,"visible":true,"origin":"","legend":"","description":"","filename":"zip2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7111581/v1_covered_a673b2af-aa41-43a7-9ba8-5ba15b76be97.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Q-CMAPO: A quantum-classical framework for balancing exploration and exploitation in multi-agent reinforcement learning","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"quantum-machine-intelligence","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"qumi","sideBox":"Learn more about [Quantum Machine Intelligence](http://link.springer.com/journal/42484)","snPcode":"42484","submissionUrl":"https://submission.nature.com/new-submission/42484/3","title":"Quantum Machine Intelligence","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Quantum optimization, Multi-agent reinforcement learning, Exploration, exploitation, Unmanned aerial vehicle","lastPublishedDoi":"10.21203/rs.3.rs-7111581/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7111581/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, we propose a novel approach, Q-CMAPO (Quantum-Classical Multi-agent Policy Optimization), for tackling complex decision-making problems in multi-agent systems. By leveraging quantum-inspired optimization techniques, Q-CMAPO efficiently addresses the exploration-exploitation tradeoff, enhancing the scalability and performance of reinforcement learning (RL) algorithms in partially observable, non-stationary environments. We introduce an innovative framework that combines centralized training with decentralized execution (CTDE), enabling seamless cooperation between agents while preserving their autonomy during execution. Through extensive empirical evaluation, including various UAV deployment scenarios, we demonstrate that Q-CMAPO consistently outperforms existing baselines in both computational efficiency and classification accuracy. Our experiments show significant improvements in performance metrics, as well as substantial gains in runtime efficiency and memory utilization. Furthermore, we provide a comprehensive theoretical analysis, proving the convergence and stability of the proposed method in non-stationary environments. We also conduct an ablation study, shedding light on the importance of different components of Q-CMAPO in optimizing agent cooperation. While promising, the proposed approach faces several challenges, including its sensitivity to hyperparameters and scalability in large-scale systems, suggesting opportunities for future refinement and expansion. The integration of Q-CMAPO into real-world applications, such as autonomous robotics, and UAV-based surveillance, opens new avenues for research, bridging the gap between quantum-inspired optimization and practical deployment in multi-agent systems.\u003c/p\u003e","manuscriptTitle":"Q-CMAPO: A quantum-classical framework for balancing exploration and exploitation in multi-agent reinforcement learning","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-29 12:52:49","doi":"10.21203/rs.3.rs-7111581/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"169783197319871577978501439168658013059","date":"2025-07-28T04:47:31+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"31329782668588335491825238002232386088","date":"2025-07-28T03:34:31+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-07-28T03:03:55+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-07-22T15:52:40+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-07-15T08:35:44+00:00","index":"","fulltext":""},{"type":"submitted","content":"Quantum Machine Intelligence","date":"2025-07-13T06:24:20+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"quantum-machine-intelligence","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"qumi","sideBox":"Learn more about [Quantum Machine Intelligence](http://link.springer.com/journal/42484)","snPcode":"42484","submissionUrl":"https://submission.nature.com/new-submission/42484/3","title":"Quantum Machine Intelligence","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"79a093f2-8393-457d-a888-647dade2f888","owner":[],"postedDate":"July 29th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-02-09T16:13:06+00:00","versionOfRecord":{"articleIdentity":"rs-7111581","link":"https://doi.org/10.1007/s42484-026-00361-0","journal":{"identity":"quantum-machine-intelligence","isVorOnly":false,"title":"Quantum Machine Intelligence"},"publishedOn":"2026-02-03 15:57:51","publishedOnDateReadable":"February 3rd, 2026"},"versionCreatedAt":"2025-07-29 12:52:49","video":"","vorDoi":"10.1007/s42484-026-00361-0","vorDoiUrl":"https://doi.org/10.1007/s42484-026-00361-0","workflowStages":[]},"version":"v1","identity":"rs-7111581","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7111581","identity":"rs-7111581","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}