Probability Seminars——On the global convergence of a randomly perturbed dissipative nonlinear oscillator
主 题: Probability Seminars——On the global convergence of a randomly perturbed dissipative nonlinear oscillator
报告人: Dr. Junchi Li (Princeton University)
时 间: 2017-12-26 10:00-11:00
地 点: Room 1303, Sciences Building No. 1
Abstract: We consider in this work small random perturbations of a nonlinear oscillator with friction–type dissipation. We rigorously prove that under non–degenerate perturbations of multiplicative noise type, the perturbed system that describes the dynamics of the dissipative oscillator converges to local minimizers of the potential function in O(ln(1/\eps)) time on average, where \eps > 0 is the scale of the random perturbation. Under a change of time scale, this indicates that for the di?usion process that approximates the stochastic heavy–ball method, it takes (up to logarithmic factor) only a linear time of the square root of inverse stepsize to evade from all saddle points and hence it implies a fast convergence of its discrete-time counterpart. This is a joint work with Wenqing Hu* and Weijie Su.