Instructor: Ben Recht
Time: M 1-4 PM
Location: 310 Soda Hall
Description: This course investigates the foundations of information, learning, and adaptation in the design and study of complex feedback systems. We will study notions of robustness, adaptivity, and optimization in feedback systems, and their associated principles, advantages, and disadvantages. We will compare the trade-offs between rich hierarchical modeling of complex systems and purely data-driven models for analysis and planning. In tandem, we will explore the roles of forecasting, estimation, predictive modeling, and retraining in automated decision making for these systems. The goal of the course will be to draw together disparate perspectives and evaluation metrics across control, machine learning, and decision theory to make sense of how we interact with complex, dynamic processes.
Prerequisites: The technical content of this class sits at the intersection of machine learning and control theory. Introductory graduate background in both topics (e.g., CS281A and EE221A) is a required prerequisite.
Logistics: The course will meet once weekly and be run as a seminar. Students will be expected to scribe lecture notes, deliver a presentation on a paper related to the course material, and complete a project.
Blog: Ben will host a Class Live Blog on argmin.net.
For enrolled students: Detailed information regarding assignments, assessments, and logistics can be found on bcourses.
References:
(AR) Astrom, Karl J. “Model Uncertainty and Robust Control.” 2000.
(AH) Astrom, Karl J. and Tore Hagglund. Advanced PID Control. Instrumentation, Systems, and Automation Society. 2006.
(DFT) Doyle, John C., Bruce A. Francis, and Allen R. Tannenbaum. Feedback Control Theory. Macmillan Publishing Co., 1990.
(PPA) Hardt, Moritz and Benjamin Recht Patterns, Predictions, and Actions. Foundations of Machine Learning. Princeton University Press, 2022.
(Wil) Willems, J. C. “The Behavioral Approach to Open and Interconnected Systems.” IEEE Control Systems Magazine, vol. 27, no. 6, pp. 46-99, 2007.
(Opt4DA) Wright, S. and Benjamin Recht Optimization for Data Analysis. Cambridge University Press, 2022.
01-26-2026 - Feedback systems and interconnection
Readings: DFT Chapters 2 and 3
Wil pp 47-51
Old Blog: The Soothing Warmth of Vacuum Tubes
Lecture Blog 1: Links and Loops
Lecture Blog 2: Sweet spots for analysis
02-02-2026 - Stability
Readings: Lecture Notes
S. Boyd. Basic Lyapunov Theory
Bof et al. Lyapunov Theory for Discrete Time Systems
L. Lessard. Lyapunov Functions
Lecture Blog 1: Matters of Life and Death
Lecture Blog 2: All Downhill From Here
02-09-2026 - PID in control and learning
Readings: AH Chapter 3
Laurent Lessard, Benjamin Recht, and Andrew Packard.(2016) “Analysis and Design of Optimization Algorithms via Integral Quadratic Constraints.” SIAM Journal on Optimization, 26(1), 57-95.
Alexandre Megretski and Anders Rantzer. (1997) “System analysis via integral quadratic constraints.” IEEE Transactions on Automatic Control, 42(6), 819-830.
Opt4DA Sections 4.0-4.4
Lecture Blog: Advanced Simplicity
Lecture Blog: Searching for Stability
02-23-2026 - Policy optimization
Readings: PPA Chapter 11 and the section on Direct Policy Search in Chapter 12
S. Boyd. Linear quadratic regulator: Discrete-time finite horizon
Lecture Blog: Maximum Principles
03-02-2026 - Robustness, Fragility, and Vibes of Optimal Control
Readings: equivalence of H2 and LQR
LQR gain margins: robustness for free?
LQG gain margins: there are none.
Lecture Blog: At Least It’s an Ethos?
03-16-2026 - System identification
Readings: AR Section “How to Compare two Systems.”
Simchowitz, M., Mania, H., Tu, S., Jordan, M. I., & Recht, B. (2018). “Learning without mixing: Towards a sharp analysis of linear system identification.” In Conference On Learning Theory.
Verhaegen, M., & Dewilde, P. (1992). “Subspace model identification Part 1. The output-error state-space model identification class of algorithms.” International Journal of Control, 56(5), 1187–1210.
Lecture Blog: Small World Models.
03-30-2026 - Action impact tradeoffs
04-06-2026 - Forecasting
04-13-2026 - World Models and actions from simulation
04-20-2026 - Architectures for feedback
04-27-2026 - Class presentations