December 5, 2019

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EPFL Course - Optimization for Machine Learning - CS-439

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EPFL Course - Optimization for Machine Learning - CS-439

Official coursebook information

Lectures: Fri 13:15-15:00 in CO2

Exercises: Fri 15:15-17:00 in BC01

This course teaches an overview of modern mathematical optimization methods, for applications in machine learning and data science. In particular, scalability of algorithms to large datasets will be discussed in theory and in implementation.



Convexity, Gradient Methods, Proximal algorithms, Subgradient Methods, Stochastic and Online Variants of mentioned methods, Coordinate Descent, Frank-Wolfe, Accelerated Methods, Primal-Dual context and certificates, Lagrange and Fenchel Duality, Second-Order Methods including Quasi-Newton Methods, Derivative-Free Optimization.

Advanced Contents:

Parallel and Distributed Optimization Algorithms

Computational Trade-Offs (Time vs Data vs Accuracy), Lower Bounds

Non-Convex Optimization: Convergence to Critical Points, Alternating minimization, Neural network training


Nr Date Topic Materials Exercises
#1 21.2. Introduction, Convexity notes, slides lab01
#2 28.2. Gradient Descent notes, slides lab02
#3 6.3. Projected Gradient Descent notes, slides lab03
#4 13.3. Proximal and Subgradient Descent notes, slides lab04
#5 20.3. Stochastic Gradient Descent, Non-Convex Optimization notes, slides lab05
#6 27.3. Non-Convex Optimization, Accelerated Gradient Descent notes, slides lab06
#7 3.4. Non-Convex Opt., Newton’s Method
. 10.4. easter vacation -
. 17.4. easter vacation -
#8 24.4. Newton & Quasi-Newton
#9 1.5. Frank-Wolfe
#10 8.5. Coordinate Descent
#11 15.5. Duality, Gradient-free methods, Applications
#12 22.5. Opt for ML in Practice
#13 29.5. Mini-Project week


The weekly exercises consist of a mix of theoretical and practical Python exercises for the corresponding topic each week (starting week 2). Solutions to theory exercises are available here, and for practicals in the lab folder.


A mini-project will focus on the practical implementation: Here we encourage students to investigate the real-world performance of one of the studied optimization algorithms or variants, helping to provide solid empirical evidence for some behaviour aspects on a real machine-learning task. The project is mandatory and done in groups of 3 students. It will count 20% to the final grade. Project reports (3 page PDF) are due May 29th. Here is a detailed project description.


Final written exam in exam session, summer 2020. Format: Closed book. Theoretical questions similar to exercises. You are allowed to bring one cheat sheet (A4 size paper, both sides can be used), either handwritten or 11 point minimum font size. For practice: exam 2019, solutions 2019, exam 2018.

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