{"paper":{"title":"Instance-Adaptive Online Multicalibration","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A single efficient algorithm achieves online multicalibration with error rates that automatically adapt to the complexity of the data sequence.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Aaron Roth, Claire Jie Zhang, Jamie Morgenstern, Zhiming Huang","submitted_at":"2026-05-10T02:45:59Z","abstract_excerpt":"We study online multicalibration beyond the worst-case. We give a single, efficient algorithm which dynamically interpolates between benign and worst-case sequences by adaptively refining a dyadic grid of prediction values. Its error is controlled by the number of leaves in the refinement tree. Our analysis recovers the known $\\widetilde O(T^{2/3})$ worst-case-optimal rate for online multicalibration, while simultaneously automatically adapting to easier instances: in the marginal stochastic setting it obtains a rate of $\\widetilde O(\\sqrt T)$, and for piecewise-stationary means with $J$ segme"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We give a single, efficient algorithm which dynamically interpolates between benign and worst-case sequences by adaptively refining a dyadic grid of prediction values. Its error is controlled by the number of leaves in the refinement tree. ... the rate depends on a threshold-complexity measure of the predictable mean process relative to the group family. We show that this dependence is tight up to logarithmic factors.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The analysis assumes that the threshold-complexity measure of the predictable mean process (relative to the given group family) is well-defined and that the algorithm can observe enough information to decide when to refine the dyadic grid without additional side information.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A single online multicalibration algorithm adaptively refines a dyadic grid and achieves instance-dependent rates: O(T^{2/3}) worst-case, O(sqrt T) for marginal stochastic data, and O(sqrt(JT)) for J-piecewise stationary means.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A single efficient algorithm achieves online multicalibration with error rates that automatically adapt to the complexity of the data sequence.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"7e50624eeae355e9a114ab44314402bd943ed7a13d27665a83a4cce2e8c20e1d"},"source":{"id":"2605.09273","kind":"arxiv","version":2},"verdict":{"id":"0283a81d-f593-4251-8a3b-1706394b515e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T04:39:51.056389Z","strongest_claim":"We give a single, efficient algorithm which dynamically interpolates between benign and worst-case sequences by adaptively refining a dyadic grid of prediction values. Its error is controlled by the number of leaves in the refinement tree. ... the rate depends on a threshold-complexity measure of the predictable mean process relative to the group family. We show that this dependence is tight up to logarithmic factors.","one_line_summary":"A single online multicalibration algorithm adaptively refines a dyadic grid and achieves instance-dependent rates: O(T^{2/3}) worst-case, O(sqrt T) for marginal stochastic data, and O(sqrt(JT)) for J-piecewise stationary means.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The analysis assumes that the threshold-complexity measure of the predictable mean process (relative to the given group family) is well-defined and that the algorithm can observe enough information to decide when to refine the dyadic grid without additional side information.","pith_extraction_headline":"A single efficient algorithm achieves online multicalibration with error rates that automatically adapt to the complexity of the data sequence."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.09273/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T08:02:08.914613Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T20:34:28.985734Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T13:31:17.808759Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T10:22:16.618251Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"63a0e1f4c96243ebbcc85ade7f4d5204a5985f254a6c502c15069f71c6371b0d"},"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"}