Adaptime step size in Monte Carlo methods

Suppose that I have an hamiltonian H(x,y), and I would like to use
Monte Carlo (Metropolis) to sample averages in the the Bolzmann
ensemble. Assume that it is cheap to do a step on the form

(x,y) -> (x+dx(2*rand-1),y)

But it is expensive to do a step on the form

(x,y) -> (x,y+dy(2*rand-1))

Is there literature on adaptive algorithms to find the right stepsizes
dx and dy and to choose the right number of x steps per y-step? I can
come up with simpleminded ideas, but I have a fear that the step size
control may give some unwanted feedback on the dynamics if microscopic
reversebility is not observed.

Niels

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