EE 227C (Spring 2018)
Convex Optimization and Approximation

University of California, Berkeley

Time: TuTh 12:30PM - 1:59PM, Location: Etcheverry 3106
Instructor: Moritz Hardt (Email: hardt+ee227c@berk…edu)
Graduate Instructor: Max Simchowitz (Email: msimchow@berk…edu).
Office hours: Max on Mon 3-4pm, Soda 310 (starting 1/29), Moritz on Fri 9–9:50a, SDH 722

Summary

This course will explore theory and algorithms for nonlinear optimization. We will focus on problems that arise in machine learning and modern data analysis, paying attention to concerns about complexity, robustness, and implementation in these domains. We will also see how tools from convex optimization can help tackle non-convex optimization problems common in practice.

Assignments

Assignments will be posted on Piazza. If you haven’t already, sign up here. Homeworks will be assigned roughly every two weeks, and 2–3 problems will be selected for grading (we will not tell you which ones in advance). Assignments should be submitted through GradeScope; the course is listed as EE227C, which you may join with entry code 9P5NDV. All homeworks should be latexed. Students will be permitted two unexcused late assignments (up to a week late). Students requesting additional extensions should email Max.

Grading

Grading policy: 50% homeworks, 10% scribing, 20% midterm exam, 20% final exam.

Course notes

Course notes will be publicly available. Participants will collaboratively create and maintain notes over the course of the semester using git. See this repository for source files. Most lectures will have an accompanying Jupyter notebook containing plots and illustrative examples.

Sign up for scribing here

All three scribes should collaborate to provide a single tex file as seen here. Students are required to closely follow these instructions.

We suggest that each scribe takes down notes, and then all three meet after class to consolidate.

All available lecture notes (pdf)

See individual lectures below. These notes likely contain several mistakes. If you spot any please send an email or pull request.

Schedule

# Date Topic pdf ipynb
    Part I: Basic gradient methods    
1 1/16 Convexity pdf ipynb
2 1/18 Gradient method (non-smooth and smooth) pdf
3 1/23 Gradient method (strongly convex) pdf
4 1/25 Some applications of gradient methods pdf ipynb
5 1/30 Conditional gradient (Frank-Wolfe algorithm) pdf ipynb
    Part II: Krylov methods and acceleration    
6 2/1 Discovering acceleration with Chebyshev polynomials pdf ipynb
7 2/6 Nesterov’s accelerated gradient descent pdf
8 2/8 Eigenvalue intermezzo pdf
9 2/13 Lower bounds, robustness vs acceleration pdf py
    Part III: Stochastic optimization    
10 2/15 Stochastc optimization pdf
11 2/20 Learning, regularization, and generalization pdf
12 2/22 Coordinate Descent (guest lecture by Max Simchowitz) pdf
    Part IV: Dual methods    
13 2/27 Duality theory pdf
14 3/1 Dual decomposition, method of multipliers pdf
15 3/6 Stochastic Dual Coordinate Ascent pdf
16 3/8 Backpropagation and adjoints pdf
    Part V: Non-convex problems    
17 3/13 Non-convex problems pdf
18 3/15 Saddle points pdf  
19 3/20 Alternating minimization and expectaction maximization ipynb
20 3/22 Derivative-free optimization, policy gradient, controls ipynb
3/27 No class (Spring break)    
3/29 No class (Spring break)    
21 4/3 Guest lecture by Ludwig Schmidt on non-convex constraints pdf  
22 4/5 Guest lecture by Ludwig Schmidt on non-convex constraints   ipynb
    Part VI: Higher-order and interior point methods    
23 4/10 Newton method    
24 4/12 Second-order methods code ipynb
25 4/17 Barrier methods    
26 4/19 Primal-dual interior point methods    
27 4/24 Sum of squares    
28 4/26 Last lecture    
29 5/1 Reading, review, recitation    
30 5/3 Reading, review, recitation    

Background

The prerequisites are previous coursework in linear algebra, multivariate calculus, probability and statistics. Coursework or background in optimization theory as covered in EE227BT is highly recommended. The class will involve some basic programming. Students are encouraged to use either Julia or Python. We discourage the use of MATLAB.

Material

Textbooks

Lecture notes

Blog posts