{"paper":{"title":"On Stopping Times of Power-one Sequential Tests: Tight Lower and Upper Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Aaditya Ramdas, Shubhada Agrawal","submitted_at":"2025-04-28T16:22:54Z","abstract_excerpt":"We prove two lower bounds for stopping times of sequential tests between general composite nulls and alternatives. The first lower bound is for the setting where the type-1 error level $\\alpha$ approaches zero, and equals $\\log(1/\\alpha)$ divided by a certain infimum KL divergence, termed $\\operatorname{KL_{inf}}$. The second lower bound applies to the setting where $\\alpha$ is fixed and $\\operatorname{KL_{inf}}$ approaches 0 (meaning that the null and alternative sets are not separated) and equals $c \\operatorname{KL_{inf}}^{-1} \\log \\log \\operatorname{KL_{inf}}^{-1}$ for a universal constant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.19952","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/2504.19952/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"}