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：我们开发了一类基于随机化Nesterov方案的新型MCMC算法。通过适当添加噪声，得到了一个时间非齐次的欠阻尼朗之万方程，并证明该方程以指定目标分布作为其不变测度。同时建立了在Wasserstein-2距离下收敛至平稳分布的速率。还提供了所提出朗之万动力学的Metropolis调整和随机梯度版本。实验表明，对于统计和图像处理中的不同模型，所提方法相较于典型朗之万采样器具有更优性能，包括所得马尔可夫链更好的混合性。