{"paper":{"title":"Misspecified Universal Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Misspecified universal learning with log-loss admits an optimal learner derived from minimax regret analysis.","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Meir Feder, Shlomi Vituri","submitted_at":"2026-05-11T09:44:02Z","abstract_excerpt":"This paper addresses the problem of universal learning under model misspecification with log-loss. In this setting, the learner operates with a hypothesis class of models denoted by $\\Theta$, while the true data-generating process belongs to a broader class $\\Phi \\supset \\Theta$, and may lie outside the assumed hypothesis space. Classical approaches have characterized the minimax regret and identified optimal universal learners in both the well-specified stochastic and individual deterministic frameworks. The misspecified setting has received comparatively less attention, although several impo"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We analyze the minimax regret in the misspecified setting and derive the corresponding optimal universal learner. 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We propose this formulation as a unified framework for universal learning, applicable to any form of uncertainty in the data-generating process, across both online and batch data arrival modes, as well as supervised and unsupervised learning tasks.","one_line_summary":"Minimax regret is characterized for misspecified universal learning with log-loss, yielding the optimal universal learner as a unified framework for any uncertainty in the data-generating process.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the minimax regret analysis and optimal learner derivation from the well-specified case extend directly to the misspecified case Φ ⊃ Θ without introducing new technical obstacles or requiring additional assumptions on the relationship between Θ and Φ.","pith_extraction_headline":"Misspecified universal learning with log-loss admits an optimal learner derived from minimax regret analysis."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.10282/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T06:22:00.846301Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T15:37:14.381885Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T11:31:19.312816Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T09:29:42.503975Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"f6f6ccb91ec99a4d83a4197de3626e8e718c59420589afdd874da2c8f23f9c6b"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}