论文标题
关于模拟退火的广义Langevin方程
On the Generalised Langevin Equation for Simulated Annealing
论文作者
论文摘要
在本文中，我们考虑了通用（高阶）兰格文方程，以模拟非凸功能的退火和优化。我们的方法通过使用适当的Ornstein-Uhlenbeck过程代替Brownian噪声来修改不足的Langevin方程，以说明系统中的内存。在合理的损耗函数和退火时间表的条件下，我们将连续的时间动力学融合到全球最小值。此外，与阻尼和阻尼不足的Langevin动力学相比，我们对状态空间进行了数值调查，并显示出更好的性能和更高的状态探索。
In this paper, we consider the generalised (higher order) Langevin equation for the purpose of simulated annealing and optimisation of nonconvex functions. Our approach modifies the underdamped Langevin equation by replacing the Brownian noise with an appropriate Ornstein-Uhlenbeck process to account for memory in the system. Under reasonable conditions on the loss function and the annealing schedule, we establish convergence of the continuous time dynamics to a global minimum. In addition, we investigate the performance numerically and show better performance and higher exploration of the state space compared to the underdamped and overdamped Langevin dynamics with the same annealing schedule.
