1 research outputs found
Mixing Time Estimation in Ergodic Markov Chains from a Single Trajectory with Contraction Methods
The mixing time of an ergodic Markov chain measures the
rate of convergence towards its stationary distribution . We
consider the problem of estimating from one single
trajectory of observations , in the case where the
transition kernel is unknown, a research program started by
Hsu et al. [2015]. The community has so far focused primarily on leveraging
spectral methods to estimate the relaxation time of a
reversible Markov chain as a proxy for . Although these
techniques have recently been extended to tackle non-reversible chains, this
general setting remains much less understood. Our new approach based on
contraction methods is the first that aims at directly estimating
up to multiplicative small universal constants instead of
. It does so by introducing a generalized version of
Dobrushin's contraction coefficient , which is shown to
control the mixing time regardless of reversibility. We subsequently design
fully data-dependent high confidence intervals around
that generally yield better convergence guarantees and are more practical than
state-of-the-art.Comment: Accepted for presentation at ALT202