This paper presents a methodology and numerical algorithms for constructing accelerated gradient flows on the space of probability distributions. In particular, we extend the recent variational formulation of accelerated methods in (Wibisono et al., 2016) from vector valued variables to probability distributions. The variational problem is modeled as a mean-field optimal control problem. A quantitative estimate on the asymptotic convergence rate is provided based on a Lyapunov function construction, when the objective functional is displacement convex. An important special case is considered where the objective functional is the relative entropy. For this case, two numerical approximations are presented to implement the Hamilton's equations as a system of N interacting particles. The algorithm is numerically illustrated and compared with the MCMC and Hamiltonian MCMC algorithms.
Amir Taghvaei (University of Illinois at Urbana-Champaign)
Amirhossein Taghvaei was born and raised in southern beach of Caspian sea, Mazandaran, Iran. After obtaining two B.S degrees in Mechanical engineering and Physics from Sharif Univ. of Technology, Tehran, Iran, he joined University of Illinois at Urbana-Champaign as a PhD student in Mechanical Science and Engineering department. While pursuing PhD, he obtained his Masters degree in Mathematics, in May 2017. He is now in the last stage of his PhD program looking for opportunities to continue an academic path. He is a member of the Decision and Control group in Coordinated Science Laboratory advised by Prof. Prashant Mehta. His research interest lies mostly in the intersection of control theory and machine learning.
Prashant Mehta (University of Illinois at Urbana-CHampaign)
Related Events (a corresponding poster, oral, or spotlight)
2019 Oral: Accelerated Flow for Probability Distributions »
Thu Jun 13th 10:15 -- 10:20 AM Room Room 101