Bayesian Optimization for Adaptive MCMC
  This paper proposes a new randomized strategy for adaptive MCMC using Bayesian optimization. This approach applies to non-differentiable objective functions and trades off exploration and exploitation to reduce the number of potentially costly objective function evaluations. We demonstrate the strategy in the complex setting of sampling from constrained, discrete and densely connected probabilistic graphical models where, for each variation of the problem, one needs to adjust the parameters of the proposal mechanism automatically to ensure efficient mixing of the Markov chains. 
Nimalan Mahendran, Ziyu Wang, Firas Hamze, Nando de Freitas
stat.CO stat.ML