ECE 586: Stochastic Differential Equations
in Optimization, Control, and Learning (Spring 2023)

Maxim Raginsky (maxim at illinois dot edu)
Teaching Assistant
Joshua Hanson (jmh4 at illinois dot edu)

About this course
Regular weekly schedule
Academic integrity policies


February 23
February 22
February 16
February 2
January 30
January 13

About this course

What is this?
Stochastic Differential Equations in Optimization, Control, and Learning is an advanced graduate course introducing theory and engineering applications of stochastic differential equations. The following fundamental topics will be covered: Brownian motion and diffusion processes; forward Kolmogorov (Fokker-Planck) and backward Kolmogorov equations; stochastic integrals of Itô and Stratonovich; change of measure (Cameron-Martin-Girsanov theory); and the Feynman-Kac formula. The theoretical concepts will be illustrated and developed through applications to stochastic control (the Kalman-Bucy filter and the LQG problem, nonlinear filters, Hamilton-Jacobi-Bellman equation for controlled diffusions), optimization (Langevin dynamics and simulated annealing in continuous time), and machine learning (sampling via the Schrödinger bridge and score-based generative models). Prerequisites include probability and random processes, multivariable calculus, and linear algebra. Other material and background will be introduced as needed.
There is no official textbook. The material in this course will be based on a number of sources, including: Additional readings and instructor's course notes will be provided during the semester.
Grades will be based on homework (60%) and a written report (40%).

Regular weekly schedule

Tue Thu 9:30-10:50 am, 2017 ECEB
Office hours:
instructor Thursdays, 11am-noon, 162 CSL
TA Tuesdays, 11am-noon, 146 CSL
Due Thursdays, by the end of the day
Homeworks are released at least one week before the due date.