We study a sequential Monte Carlo algorithm to sample from the Gibbs measure with a non-convex energy function at a low temperature. We use the practical and popular geometric annealing schedule, and use a Langevin diffusion at each temperature level. The Langevin diffusion only needs to run for a time that is long enough to ensure local mixing within energy valleys, which is much shorter than the time required for global mixing. Our main result shows convergence of Monte Carlo estimators with time complexity that, approximately, scales like the fourth power of the inverse temperature, and the square of the inverse allowed error. We also study this algorithm in an illustrative model scenario where more explicit estimates can be given.

翻译：本文研究了一种序列蒙特卡洛算法，用于在低温下从具有非凸能量函数的吉布斯测度中采样。我们采用实用且常用的几何退火调度方案，并在每个温度层级上使用朗之万扩散过程。朗之万扩散仅需运行足够长的时间以确保能量谷内的局部混合，该时间远短于全局混合所需的时间。我们的主要结果表明，蒙特卡洛估计量的收敛时间复杂度近似地按逆温度的四次方与允许误差倒数的平方进行缩放。我们还在一个可给出更显式估计的示例模型场景中研究了该算法的性能。