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Text
(Email:
msimchow@berk…edu). Office hours: Max on Mon 3-4pm, Soda 310 (starting 1/29), Moritz on Fri 9–9:50a, SDH 722SUMMARY
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.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 repositoryfor
source files.
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
IPYNB
PART I: BASIC GRADIENT METHODS1
1/16
Convexity
ipynb
2
1/18
Gradient method (non-smooth and smooth)—
3
1/23
Gradient method (strongly convex)—
4
1/25
Some applications of gradient methodsipynb
5
1/30
Conditional gradient (Frank-Wolfe algorithm)ipynb
PART II: KRYLOV METHODS AND ACCELERATION6
2/1
Discovering acceleration with Chebyshev polynomialsipynb
7
2/8
Eigenvalue intermezzo—
8
2/6
Nesterov’s accelerated gradient descent—
9
2/13
Lower bounds, robustness vs accelerationpy
PART III: STOCHASTIC OPTIMIZATION10
2/15
Stochastc optimization—
11
2/20
Learning, regularization, and generalization—
12
2/22
Coordinate Descent (guest lecture by Max Simchowitz)—
PART IV: DUAL METHODS13
2/27
Duality theory
—
14
3/1
Dual decomposition, method of multipliers—
15
3/6
Stochastic Dual Coordinate Ascent—
16
3/8
Backpropagation and adjoints—
PART V: NON-CONVEX PROBLEMS17
3/13
Non-convex problems
—
18
3/15
Saddle points
—
19
3/20
Alternating minimization and expectaction maximization—
ipynb
20
3/22
Derivative-free optimization, policy gradient, controls—
ipynb
21
4/3
Non-convex constraints I (guest lecture by Ludwig Schmidt)22
4/5
Non-convex constraints II (guest lecture by Ludwig Schmidt)ipynb
PART VI: HIGHER-ORDER AND INTERIOR POINT METHODS23
4/10
Newton’s method
—
24
4/12
Experimenting with second-order methods—
ipynb
25
4/17
Enter interior point methods—
26
4/19
Primal-dual interior point methods—
27
4/24
Ellipsoid method
—
28
4/26
Submodular functions, Lovasz extension—
29
5/1
Reading, review, recitation30
5/3
Reading, review, recitation SIGN UP FOR SCRIBING HERE All three scribes should collaborate to provide a _single_ tex file asseen 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.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 emailMax.
GRADING
Grading policy: 50% homeworks, 10% scribing, 20% midterm exam, 20%final exam.
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
* Nonlinear Programming (3rd edition). D. Bertsekas, AthenaScientific.
* Numerical Optimization. J. Nocedal and S. J. Wright, Springer Series in Operations Research, Springer-Verlag, New York, 2006 (2ndedition).
* Convex Optimization. S. Boyd and L. Vandenberghe. Cambridge University Press, Cambridge, 2003. PDF available here * Introductory Lectures on Convex Optimization: A Basic Course. Y. Nesterov. Kluwer, 2004. * Convex Optimization: Algorithms and Complexity. S. Bubeck. PDFavailable here
* Nonlinear Programming D. P. Bertsekas. Athena Scientific, Belmont, Massachusetts. (2nd edition). 1999. * Efficient Methods in Convex Programming. A. Nemirovski. Lecture Notes as PDF available here.
Details
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