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.
Large deviations, hypotheses testing, a nd source coding for finite Markov chains,
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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.