论文标题
反射梯度Langevin动力学的收敛误差分析，用于全球优化非凸的约束问题
Convergence Error Analysis of Reflected Gradient Langevin Dynamics for Globally Optimizing Non-Convex Constrained Problems
论文作者
论文摘要
梯度Langevin动力学及其各种变体因其与全球最佳解决方案的融合而引起了越来越多的关注，最初是在不受约束的凸框架中，而最近在凸的约束非凸面问题中。在目前的工作中，我们将这些框架扩展到非凸的可行区域上的非凸问题，其全局优化算法建立在反射的梯度Langevin Dynamics上并得出其收敛速率。通过有效利用其在边界上的反射与Neumann边界条件的泊松方程的概率表示结合，我们提出了有希望的收敛速率，尤其是比现有的，对于凸由凸的非凸面问题而言，尤其是比现有的。
Gradient Langevin dynamics and a variety of its variants have attracted increasing attention owing to their convergence towards the global optimal solution, initially in the unconstrained convex framework while recently even in convex constrained non-convex problems. In the present work, we extend those frameworks to non-convex problems on a non-convex feasible region with a global optimization algorithm built upon reflected gradient Langevin dynamics and derive its convergence rates. By effectively making use of its reflection at the boundary in combination with the probabilistic representation for the Poisson equation with the Neumann boundary condition, we present promising convergence rates, particularly faster than the existing one for convex constrained non-convex problems.
