论文标题
惩罚Langevin动力学，以消失的惩罚对光滑和原木目标的罚款
Penalized Langevin dynamics with vanishing penalty for smooth and log-concave targets
论文作者
论文摘要
我们研究了通过凸面和平稳的潜在函数定义的$ \ mathbb r^p $进行抽样的问题。我们考虑一个连续的扩散型过程，称为受惩罚的langevin Dynamics（PLD），其漂移是电势的负梯度，以及在时间到达无限时消失的线性惩罚。在时间$ t $的PLD分布与目标之间的wasserstein-2距离上的上限是建立的。该上限突出了惩罚衰减速度对近似准确性的影响。结果，考虑到低温限制，我们推断出了新的非沉淀性保证，以促成优化问题的惩罚梯度流的收敛性。
We study the problem of sampling from a probability distribution on $\mathbb R^p$ defined via a convex and smooth potential function. We consider a continuous-time diffusion-type process, termed Penalized Langevin dynamics (PLD), the drift of which is the negative gradient of the potential plus a linear penalty that vanishes when time goes to infinity. An upper bound on the Wasserstein-2 distance between the distribution of the PLD at time $t$ and the target is established. This upper bound highlights the influence of the speed of decay of the penalty on the accuracy of the approximation. As a consequence, considering the low-temperature limit we infer a new nonasymptotic guarantee of convergence of the penalized gradient flow for the optimization problem.
