Improving sample efficiency of high dimensional Bayesian optimization
  with MCMC
Zeji Yi Yunyue Wei Chu Xin Cheng Kaibo He Yanan Sui
Sequential optimization methods are often confronted with the curse of
dimensionality in high-dimensional spaces. Current approaches under the
Gaussian process framework are still burdened by the computational complexity
of tracking Gaussian process posteriors and need to partition the optimization
problem into small regions to ensure exploration or assume an underlying
low-dimensional structure. With the idea of transiting the candidate points
towards more promising positions, we propose a new method based on Markov Chain
Monte Carlo to efficiently sample from an approximated posterior. We provide
theoretical guarantees of its convergence in the Gaussian process Thompson
sampling setting. We also show experimentally that both the Metropolis-Hastings
and the Langevin Dynamics version of our algorithm outperform state-of-the-art
methods in high-dimensional sequential optimization and reinforcement learning
benchmarks.