Fokker-Planck Equations and Machine Learning

Yuhua Zhu, Postdoctoral Fellow, Stanford University

Feb 22, 2022

As the continuous limit of many discretized algorithms, PDEs can provide a qualitative description of algorithm's behavior and give principled theoretical insight into many mysteries in machine learning. In this talk, I will give a theoretical interpretation of several machine learning algorithms using Fokker-Planck (FP) equations. In the first one, we provide a mathematically rigorous explanation of why resampling outperforms reweighting in correcting biased data when stochastic gradient-type algorithms are used in training. In the second one, we propose a new method to alleviate the double sampling problem in model-free reinforcement learning, where the FP equation is used to do error analysis for the algorithm. In the last one, inspired by an interactive particle system whose mean-field limit is a non-linear FP equation, we develop an efficient gradient-free method that finds the global minimum exponentially fast.

Speaker Bio

Yuhua received her Ph.D. from University of Wisconsin-Madison in Mathematics. She is currently a Postdoc in Mathematics Department at Stanford University. Her general interests lie in numerical analysis, scientific computing,  interface of PDEs and machine learning, optimization and reinforcement learning. 


Susan Murphy


Jenny Mileski