{"paper":{"title":"A Two-fold Randomization Framework for Impulse Control Problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Randomized impulse control problems converge to the classical problem as the randomization parameter vanishes.","cross_cats":[],"primary_cat":"math.OC","authors_text":"Haoyang Cao, Yuchao Dong, Zhouhao Yang","submitted_at":"2025-09-15T14:58:03Z","abstract_excerpt":"We propose and analyze a randomization scheme for a general class of impulse control problems. The solution to this randomized problem is characterized as the fixed point of a compound operator which consists of a regularized nonlocal operator and a regularized stopping operator. This approach allows us to derive a semi-linear Hamilton-Jacobi-Bellman (HJB) equation. Through an equivalent randomization scheme with a Poisson compound measure, we establish a verification theorem that implies the uniqueness of the solution. Via an iterative approach, we prove the existence of the solution. The exi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The randomized impulse control problem converges to its classical counterpart as the randomization parameter λ vanishes; combined with C^{2,α}_loc regularity this confirms the framework provides a robust approximation, and the offline RL algorithm learns the randomized solution which accurately approximates the classical one.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The compound operator formed by the regularized nonlocal operator and regularized stopping operator admits a fixed point, and the equivalent Poisson compound measure scheme is valid for establishing the verification theorem (abstract, paragraph on characterization and verification).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A randomization framework for impulse control problems derives a semi-linear HJB equation, proves existence and uniqueness, shows convergence to the classical problem as lambda vanishes, and delivers an offline RL algorithm that learns accurate approximations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Randomized impulse control problems converge to the classical problem as the randomization parameter vanishes.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"cebdbfce217376a81dcc9e86c017777ad3f7c43e945c2a74707bdec882494be3"},"source":{"id":"2509.12018","kind":"arxiv","version":7},"verdict":{"id":"7e600107-a263-4d40-8a66-831162a9ecd0","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-18T16:07:19.680707Z","strongest_claim":"The randomized impulse control problem converges to its classical counterpart as the randomization parameter λ vanishes; combined with C^{2,α}_loc regularity this confirms the framework provides a robust approximation, and the offline RL algorithm learns the randomized solution which accurately approximates the classical one.","one_line_summary":"A randomization framework for impulse control problems derives a semi-linear HJB equation, proves existence and uniqueness, shows convergence to the classical problem as lambda vanishes, and delivers an offline RL algorithm that learns accurate approximations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The compound operator formed by the regularized nonlocal operator and regularized stopping operator admits a fixed point, and the equivalent Poisson compound measure scheme is valid for establishing the verification theorem (abstract, paragraph on characterization and verification).","pith_extraction_headline":"Randomized impulse control problems converge to the classical problem as the randomization parameter vanishes."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.12018/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"dd88491f0f9acefa4f2a936bf0a0a4d85ce9540c5fc34ae2ad474c0925438216"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}