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.

基于马尔可夫链蒙特卡罗方法，我们提出了一种新的算法来从近似后验中高效采样，该算法在高维度的顺序优化中表现优于现有方法。