Seminar · Summer Term 2024

Seminar on Machine Learning for Optimization (Learning to Optimize)

Lecturer
Peter Ochs
Type
Seminar for Mathematics and Computer Science
Credits
7 ECTS
Time
Tuesday 2 - 4 pm.
First meeting
23.04.2023
Teaching Assistants
Camille Castera and Sheheryar Mehmood
Language
English
Prerequisites
Basics of Mathematics (e.g. Linear Algebra 1-2, Analysis 1-3, Mathematics 1-3 for Computer Science)
Info
Basic understanding of Optimization
Info
Basics of Machine Learning are recommended but not required.

News

08.04.2024: Table of references uploaded.
11.03.2024: Webpage is online.

Description

The recently growing field of Learning to optimize (L2O) leverages machine learning techniques to develop optimization methods and shares close relations to Meta-Learning. While classic optimization algorithms are hand crafted and proved to work for certain classes of problems, L2O automates the design based on a (training) data set of typical problems. L2O approaches are data-driven and are therefore tailored to a specific distribution of problems. On one hand, this is achieved by exploiting statistical features and unlocks solution strategies that outperform classical optimization algorithms by several orders of magnitude, however, on the other hand, usually there is no or little theoretical guarantees on the actual performance for a new problem. Generalization bounds like in Empirical Risk Minimization of Statistical Learning in general can be employed to provide some evidenve for in-distribution problems. However, typically such an approach is prone to fail for out-of-distribution problems. Therefore, the worlds of L2O and classical optimization must be brought closer together to achieve reliability and speed at the same time. In this seminar, we explore some important research attempts in the world of L2O.

Registration

Register via the Seminar Assignment System at SIC Seminars.

For students from mathematics who cannnot register via this system, please write an eMail to Peter Ochs.

Requirements for Successful Participation:

Format: (in-person participation only)

Each student is assigned to three papers (assigned by us): one student gives the presentation on the paper, and the two other students take the role of moderators, i.e., they lead the discussion after the presentation.

Rules:

Documentation and Schedule

References Date
INTRO: organization, how to give good presentations, basics of optim, deep learning and training 23.04.2024
Andrychowicz, Denil, Gomez, Hoffman, Pfau, Schaul, Shillingford, de Freitas: Learning to learn by gradient descent by gradient descent, 2016.
Metz, Freeman, Harrison, Maheswaranathan, Sohl-Dickstein: Practical tradeoffs between memory, compute, and performance in learned optimizers, 2022.
Li, Malick: Learning to Optimize, 2016.
Venkatakrishnan, Bouman, Wohlberg: Plug-and-Play priors for model based reconstruction, 2013.
Meinhardt, Moeller, Hazirbas, Cremers: Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems, 2017.
Gregor, LeCun: Learning Fast Approximations of Sparse Coding, 2010.
Ablin, Moreau, Massias, Gramfort: Learning step sizes for unfolded sparse coding, 2019.
Long, Lu, Ma, Dong: PDE-Net: Learning PDEs from Data, 2017.
Heaton, Chen, Wang, Yin: Safeguarded Learned Convex Optimization, 2020.
Moeller, Möllenhoff, Cremers: Controlling Neural Networks via Energy Dissipation, 2019.
Wang, Yuan, Wu, Ge: Guarantees for Tuning the Step Size using a Learning-to-Learn Approach, 2020.
Chen, Rubanova, Bettencourt, Duvenaud: Neural Ordinary Differential Equations, 2018.
Graikos, Malkin, Jojic, Samaras: Diffusion models as plug-and-play priors, 2022.