A stochastic primal-dual method (SOMCOT) estimates the optimal-transport bisimulation distance between finite Markov chains from samples of their occupancy measures, with an O~(|X||Y|(|X|+|Y|)/((1-gamma)^2 epsilon^2)) sample-complexity guarantee.
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Distances for Markov chains from sample streams
A stochastic primal-dual method (SOMCOT) estimates the optimal-transport bisimulation distance between finite Markov chains from samples of their occupancy measures, with an O~(|X||Y|(|X|+|Y|)/((1-gamma)^2 epsilon^2)) sample-complexity guarantee.