Dynamic Inverse Optimization under Drift and Shocks: Theory, Regret Bounds, and Applications

Dynamic Inverse Optimization under Drift and Shocks: Theory, Regret Bounds, and Applications | 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 Dynamic Inverse Optimization under Drift and Shocks: Theory, Regret Bounds, and Applications Jinho Cha This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7609598/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The growing prevalence of drift and shocks in modern decision environments exposes a gap between classical optimization theory and real-world practice. Standard models assume fixed objectives, yet organizations—from hospitals to power grids—routinely adapt to shifting priorities, noisy data, and abrupt disruptions. To address this gap, this study develops a dynamic inverse optimization framework that recovers hidden, time-varying preferences from observed allocation trajectories. The framework unifies identifiability analysis with regret guarantees: conditions are established for existence and uniqueness of recovered parameters, and sharp static and dynamic regret bounds are derived to characterize responsiveness to gradual drift and sudden shocks. Methodologically, a drift-aware estimator grounded in convex analysis and online learning theory is introduced, with finite-sample guarantees on recovery accuracy. Computational experiments in healthcare, energy, logistics, and finance reveal heterogeneous recovery patterns, ranging from rapid resilience to persistent vulnerability. Overall, dynamic inverse optimization emerges as both a theoretical contribution and a broadly applicable diagnostic tool for benchmarking resilience, uncovering hidden behavioral shifts, and guiding policy interventions in complex stochastic systems. Inverse Optimization Dynamic Preferences Drift and Shocks Identifiability Dynamic Regret Decision Analytics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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-7609598","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":516522364,"identity":"3afff2b1-e814-4bd0-980c-2bf68d0df8da","order_by":0,"name":"Jinho Cha","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA70lEQVRIiWNgGAWjYBACxgYeBoYPNQw8EN4/BgYDIC1BSAvjjGNgLYwNBwyI0MIAVMzM2wDVTpQW5vazBz/bNhyWMZduPv74g4GNvDkD88HbPPgc1pOXLJ3bcJjHcs6xRKAtaYY7G9iSrfFqmcFjIJ3bd5vH4EaOIVDL4QSDAzxm0gS0GP+2bANpyf8I1PIfqIX/GyEtZtKMYC05IO8fANnChl9LT46ZZc+x/0AtaYYzzhgkG244zGZsOQePFsP2M8Y3ftSk2RvcSH7wocLATt7gePPDG2/waWnAEGLGoxwE5AnIj4JRMApGwShgYAAA2xJPn0XUAtMAAAAASUVORK5CYII=","orcid":"","institution":"Gwinnett Technical College","correspondingAuthor":true,"prefix":"","firstName":"Jinho","middleName":"","lastName":"Cha","suffix":""}],"badges":[],"createdAt":"2025-09-13 22:23:06","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7609598/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7609598/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":92212787,"identity":"204c45d9-5057-41d2-8bb2-70b97b23c23b","added_by":"auto","created_at":"2025-09-25 21:57:54","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":3338,"visible":true,"origin":"","legend":"","description":"","filename":"34ad4530b4c24c0397ee615820d01ac1.json","url":"https://assets-eu.researchsquare.com/files/rs-7609598/v1/94e3d4210550ff75a3fac07c.json"},{"id":97139637,"identity":"c5fa9129-35a6-4579-af1b-e887ab790179","added_by":"auto","created_at":"2025-12-01 10:01:26","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":9980615,"visible":true,"origin":"","legend":"","description":"","filename":"ChaManuscriptCMS.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7609598/v1_covered_bb22dcc6-d4fa-4fc4-8acc-01603cda74b8.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Dynamic Inverse Optimization under Drift and Shocks: Theory, Regret Bounds, and Applications","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Inverse Optimization, Dynamic Preferences, Drift and Shocks, Identifiability, Dynamic Regret, Decision Analytics","lastPublishedDoi":"10.21203/rs.3.rs-7609598/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7609598/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The growing prevalence of drift and shocks in modern decision environments exposes a gap between classical optimization theory and real-world practice. 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