{"paper":{"title":"Optimal sequential tests yield log-optimal e-processes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Asymptotically optimal sequential tests can be aggregated into asymptotically log-optimal e-processes using WAIT e-processes.","cross_cats":["math.PR","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Aaditya Ramdas, Ashwin Ram","submitted_at":"2026-05-12T20:27:17Z","abstract_excerpt":"It has been recently shown that e-processes are sufficient for sequential testing in the following sense: every level-$\\alpha$ sequential test can be obtained by thresholding an e-process at $1/\\alpha$. However, in the above result, neither does the test have to be asymptotically optimal (in terms of stopping times) nor does the e-process have to be asymptotically log-optimal. It has separately been shown that asymptotically log-optimal e-processes yield asymptotically optimal sequential tests. In this paper, we prove the converse, arguably completing the story: it is possible to aggregate asy"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"it is possible to aggregate asymptotically optimal sequential tests into asymptotically log-optimal e-processes. 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