Optimal policy analysis for monotonic (PO)MDPs and an application to fishery management

Optimal policy analysis for monotonic (PO)MDPs and an application to fishery management | 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 Optimal policy analysis for monotonic (PO)MDPs and an application to fishery management Jun Ju, Jerzy Filar, Dirk Kroese, Nan Ye This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6389870/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract We study the monotonicity properties of optimal policies for a class of fully/partially observable Markov Decision Processes (MDPs) motivated by renewable natural resource management. We first introduce a new class of deterministic monotonic MDPs with continuous state and action spaces, and we prove that their optimal policies are monotonic in the state. These monotonic MDPs are particularly interesting, because they do not satisfy certain supermodularity assumptions on the reward function and the transition dynamics in previous monotonicity analyses for the optimal policies of MDPs, and our proof requires an original inductive analysis. Our theoretical results are numerically illustrated on a fully observable fishery management problem, using a modified value iteration algorithm that computes near-optimal monotonic policies with a max-min smoothing strategy. We then introduce a generalization of our monotonic MDPs to handle partial observability and stochas-ticity, and we conjecture the existence of a near-optimal policy that is monotonic in the expected state. Our conjecture is supported by numerical results on a partially observable fishery management problem, using algorithms for optimizing over a class of monotonic policies called multi-threshold policies. Moreover, when the environment is unknown and needs to be learned through interactions, multi-threshold policies appear to be more robust to model learning error than general policies in a model-based offline reinforcement learning approach. Markov Processes (PO)MDPs monotonic optimal policy fishery management Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 31 Jul, 2025 Reviews received at journal 24 Jul, 2025 Reviews received at journal 20 Jul, 2025 Reviewers agreed at journal 07 Jul, 2025 Reviewers agreed at journal 05 Jul, 2025 Reviewers invited by journal 04 Jul, 2025 Editor assigned by journal 14 Apr, 2025 Submission checks completed at journal 14 Apr, 2025 First submitted to journal 06 Apr, 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-6389870","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":481698961,"identity":"73145ce3-3861-4419-839b-20f606a2a067","order_by":0,"name":"Jun Ju","email":"","orcid":"","institution":"The University of Queensland","correspondingAuthor":false,"prefix":"","firstName":"Jun","middleName":"","lastName":"Ju","suffix":""},{"id":481698962,"identity":"957dd067-60ad-41a7-a132-d2d3d19d6b38","order_by":1,"name":"Jerzy Filar","email":"","orcid":"","institution":"The University of Queensland","correspondingAuthor":false,"prefix":"","firstName":"Jerzy","middleName":"","lastName":"Filar","suffix":""},{"id":481698963,"identity":"e8efd866-25ec-431d-b8f6-656b9829b72d","order_by":2,"name":"Dirk Kroese","email":"","orcid":"","institution":"The University of Queensland","correspondingAuthor":false,"prefix":"","firstName":"Dirk","middleName":"","lastName":"Kroese","suffix":""},{"id":481698964,"identity":"dd543178-e24f-4f8a-b7fd-33a4a8da6cc7","order_by":3,"name":"Nan Ye","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAu0lEQVRIiWNgGAWjYPACGzApQYqWNNK1HCZBizn72QPMPBXnE/sOMB+8zcNgl9hASItlT14CM8+Z24kzD7AlW/MwJBPWYnAgx4CZt+124oYDPGbSPAzMRGg5/wao5d85oBb+b0At9URouQGypeEAyBY2oJbDxGh5Y3BwzrFk45mH2Ywt5xgcNybCYTmGD97U2Mn2HW9+eONNRbUsQS0gcIgHRIKjxoAY9UDA+ANEHiBS9SgYBaNgFIw8AABLjDwHZnJ1IwAAAABJRU5ErkJggg==","orcid":"","institution":"The University of Queensland","correspondingAuthor":true,"prefix":"","firstName":"Nan","middleName":"","lastName":"Ye","suffix":""}],"badges":[],"createdAt":"2025-04-07 03:53:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6389870/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6389870/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":86316692,"identity":"fd6eac39-6cc5-4769-94e8-9086973f413e","added_by":"auto","created_at":"2025-07-09 09:02:58","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1685574,"visible":true,"origin":"","legend":"","description":"","filename":"monotonicORF.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6389870/v1_covered_ddf0d6c2-f7fd-4bf9-b8a8-d671c1ca224a.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Optimal policy analysis for monotonic (PO)MDPs and an application to fishery management","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":"operations-research-forum","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Operations Research Forum](https://link.springer.com/journal/43069)","snPcode":"43069","submissionUrl":"https://submission.nature.com/new-submission/43069/3","title":"Operations Research Forum","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Markov Processes, (PO)MDPs, monotonic optimal policy, fishery management","lastPublishedDoi":"10.21203/rs.3.rs-6389870/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6389870/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We study the monotonicity properties of optimal policies for a class of fully/partially observable Markov Decision Processes (MDPs) motivated by renewable natural resource management. 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