{"paper":{"title":"Inference of Online Newton Methods with Nesterov's Accelerated Sketching","license":"http://creativecommons.org/licenses/by/4.0/","headline":"An online Newton method with Nesterov-accelerated sketching provides global convergence and asymptotic normality for inference on streaming data at first-order complexity.","cross_cats":["cs.LG","math.OC","stat.CO"],"primary_cat":"stat.ML","authors_text":"Haoxuan Wang, Sen Na, Xinchen Du","submitted_at":"2026-04-25T20:43:17Z","abstract_excerpt":"Reliable decision-making with streaming data requires principled uncertainty quantification of online methods. While first-order methods enable efficient iterate updates, their inference procedures still require updating proper (covariance) matrices, incurring $O(d^2)$ time and memory complexity, and are sensitive to ill-conditioning and noise heterogeneity of the problem. This costly inference task offers an opportunity for more robust second-order methods, which are, however, bottlenecked by solving Newton systems with $O(d^3)$ complexity. In this paper, we address this gap by studying an on"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we establish global almost-sure convergence, prove asymptotic normality of the last iterate with a limiting covariance characterized by a Lyapunov equation, and develop a fully online covariance estimator with non-asymptotic convergence guarantees.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Under standard smoothness and moment conditions","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"An accelerated sketched online Newton method with Hessian averaging achieves global almost-sure convergence, asymptotic normality via a Lyapunov covariance, and a fully online covariance estimator under standard conditions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"An online Newton method with Nesterov-accelerated sketching provides global convergence and asymptotic normality for inference on streaming data at first-order complexity.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c287889e72629a17fbf970f31da6f2e71b3f30268a40d16fa8711e052550c65f"},"source":{"id":"2604.23436","kind":"arxiv","version":2},"verdict":{"id":"c001442f-8280-44a2-a495-37e53224a965","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T07:11:48.723007Z","strongest_claim":"we establish global almost-sure convergence, prove asymptotic normality of the last iterate with a limiting covariance characterized by a Lyapunov equation, and develop a fully online covariance estimator with non-asymptotic convergence guarantees.","one_line_summary":"An accelerated sketched online Newton method with Hessian averaging achieves global almost-sure convergence, asymptotic normality via a Lyapunov covariance, and a fully online covariance estimator under standard conditions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Under standard smoothness and moment conditions","pith_extraction_headline":"An online Newton method with Nesterov-accelerated sketching provides global convergence and asymptotic normality for inference on streaming data at first-order complexity."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.23436/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T08:40:58.818825Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T23:05:34.142085Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"7e93bc226ce9fa6c2a8c4a2d38bc21a81d40a4d70a132d299fd1b5a69520e820"},"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"}