The title may seem too broad, let me specify this question a bit more.
Suppose that there is a problem that can be solved via MCMC-based algorithm, i.e., for its formulation we can construct a Markov chain, and Monte Carlo sampling is adopted to reach a desired stationary distribution.
If this MCMC algorithm has proved to work well, then is it possible that its Markov chain-based description of the problem can also be used to formulate an RL description?
If so, there is another more detailed question. Assuming that the acceptance probability in MCMC algorithm is calculated based on Metropolis-Hastings, say
$$ A(x^{\prime}, x)=\min (1, \frac{P(x^{\prime})}{P(x)} \frac{g(x\mid x^{\prime})}{g(x^{\prime}\mid x)}). $$
What could the relationship of the transition model of an RL model and this acceptance probability be?
