On the $α$-lazy version of Markov chains in estimation and testing problems

We formulate extendibility of the minimax one-trajectory length of several statistical Markov chains inference problems and give sufficient conditions for both the possibility and impossibility of such extensions. We follow up and apply this framework to recently published results on learning and identity testing of ergodic Markov chains. In particular, we show that for some of the aforementioned results, we can omit the aperiodicity requirement by simulating an $\alpha$-lazy version of the original process, and quantify the incurred cost of removing this assumption.

Identity testing of reversible Markov chains

We consider the problem of identity testing of Markov chains based on a single trajectory of observations under the distance notion introduced by Daskalakis et al. [2018a] and further analyzed by Cherapanamjeri and Bartlett [2019]. Both works made the restrictive assumption that the Markov chains under consideration are symmetric. In this work we relax the symmetry assumption to the more natural assumption of reversibility, still assuming that both the reference and the unknown Markov chains share the same stationary distribution.