A one-sided sequential test for a known Markov chain against any unknown alternative achieves SPRT-level expected stopping times when the estimator has logarithmic regret.
Generalized sequential proba bility ratio test for separate families of hypotheses,
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Sequential One-Sided Hypothesis Testing of Markov Chains
A one-sided sequential test for a known Markov chain against any unknown alternative achieves SPRT-level expected stopping times when the estimator has logarithmic regret.