{"paper":{"title":"High-Dimensional Calibration from Swap Regret","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.GT","stat.ML"],"primary_cat":"cs.LG","authors_text":"Jon Schneider, Maxwell Fishelson, Mehryar Mohri, Noah Golowich","submitted_at":"2025-05-27T17:31:47Z","abstract_excerpt":"We study the online calibration of multi-dimensional forecasts over an arbitrary convex set $\\mathcal{P} \\subset \\mathbb{R}^d$ relative to an arbitrary norm $\\Vert\\cdot\\Vert$. We connect this with the problem of external regret minimization for online linear optimization, showing that if it is possible to guarantee $O(\\sqrt{\\rho T})$ worst-case regret after $T$ rounds when actions are drawn from $\\mathcal{P}$ and losses are drawn from the dual $\\Vert \\cdot \\Vert_*$ unit norm ball, then it is also possible to obtain $\\epsilon$-calibrated forecasts after $T = \\exp(O(\\rho /\\epsilon^2))$ rounds. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21460","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/2505.21460/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"}