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We construct a new Markov chain Monte Carlo method on finite states withoptimal choices of acceptance-rejection ratio functions. We prove that theconstructed continuous time Markov jumping process has a global in-timeconvergence rate in $L^1$ distance. The convergence rate is no less thanone-half and is independent of the target distribution. For example, our methodrecovers the Metropolis-Hastings algorithm on a two-point state. And it forms anew algorithm for sampling general target distributions. Numerical examples arepresented to demonstrate the effectiveness of the proposed algorithm.

Optimal Ricci curvature Markov chain Monte Carlo methods on finite states