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

Announcements

April 20

• Homework 4 is assigned, due by the end of the day on April 27

April 12

• There will be no lecture tomorrow, April 13

March 30

• Homework 3 is assigned, due by the end of the day on April 6

March 28

• Final project info is released, available here.

February 23

• Homework 2 is assigned, due by the end of the day on March 2

February 22

• There will be no lecture tomorrow (February 23), due to CSL Student Conference

February 16

• There will be no instructor office hours today.

February 2

• Homework 1 is assigned, due by the end of the day on February 9

January 30

• The lecture notes are available here; they will be updated and revised throughout the semester.

January 13

• Welcome! Watch this space for all important course-related announcements.
• I will be away during the first week of the semester. Link to a video recording of Lecture 1 is available here.

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.

Materials

There is no official textbook. The material in this course will be based on a number of sources, including:

• W.H. Fleming and R.W. Rishel, Deterministic and Stochastic Optimal Control, Springer, 1975
• E. Wong and B. Hajek, Stochastic Processes in Engineering Systems, Springer, 1985
• J. Michael Steele, Stochastic Calculus and Financial Applications, Springer, 2001
• G.A. Pavliotis, Stochastic Processes and Applications: Diffusion Processes, the Fokker-Planck and Langevin Equations, Springer, 2014
• W. E, T. Li, and E. Vanden-Eijnden, Applied Stochastic Analysis, American Mathematical Society, 2019

Additional readings and instructor's course notes will be provided during the semester.

Coursework

Grades will be based on homework (60%) and a written report (40%).

Regular weekly schedule

Lectures

Tue Thu 9:30-10:50 am, 2017 ECEB

Office hours:

instructor	Thursdays, 11am-noon, 162 CSL
TA	Tuesdays, 11am-noon, 146 CSL

Homework

Due Thursdays, by the end of the day
Homeworks are released at least one week before the due date.