We develop a novel class of MCMC algorithms based on a stochastized Nesterov scheme. With an appropriate addition of noise, the result is a time-inhomogeneous underdamped Langevin equation, which we prove emits a specified target distribution as its invariant measure. Convergence rates to stationarity under Wasserstein-2 distance are established as well. Metropolis-adjusted and stochastic gradient versions of the proposed Langevin dynamics are also provided. Experimental illustrations show superior performance of the proposed method over typical Langevin samplers for different models in statistics and image processing including better mixing of the resulting Markov chains.

翻译：我们基于随机化Nesterov方案开发了一类新型马尔可夫链蒙特卡洛算法。通过适当添加噪声，得到时间非齐次欠阻尼朗之万方程，并证明该方程以指定目标分布作为其不变测度。同时建立了瓦瑟斯坦-2距离下的稳态收敛速率。还提供了所提朗之万动力学的Metropolis调整版本和随机梯度版本。实验表明，在统计学和图像处理的不同模型中，所提方法相较典型朗之万采样器具有更优性能，包括生成的马尔可夫链混合更充分。