{"paper":{"title":"Online Discrepancy Minimization for Sub-Gaussian Inputs via Regularization and Restriction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO","math.PR"],"primary_cat":"cs.DS","authors_text":"Nicola Wengiel","submitted_at":"2026-08-10T09:24:46Z","abstract_excerpt":"We study online discrepancy minimization: vectors $v_1,\\ldots,v_T\\in\\mathbb{R}^n$ arrive sequentially, and each must immediately be assigned a sign $x_t\\in\\{\\pm1\\}$, with the aim of minimizing $\\|\\sum_{t=1}^T x_t v_t\\|_\\infty$. We give a polynomial-time potential-based algorithm combining a regularization of the $\\ell_\\infty$-norm with restriction to an adaptively chosen coordinate set. For i.i.d. inputs with independent, symmetric, centered, unit-variance sub-Gaussian coordinates of sub-Gaussian norm at most $\\sigma$, the algorithm achieves terminal discrepancy $O(\\sigma^8\\sqrt{n})$ with prob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.10040","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.10040/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":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}