Talk of Dr. Michael Mühlebach

December 13, 2022

--- Title: Optimization with Momentum and Constraints: A Perspective from Smooth and Non-Smooth Dynamics

Time: December 13, 2022
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Dr. Michael Mühlebach
Max Planck Institute for Intelligent Systems
Tübingen, Germany


Tuesday 2022-12-13 4 p.m.
IST Seminar Room 2.255 - Pfaffenwaldring 9 - Campus Stuttgart-Vaihingen



My talk will highlight connections between dynamical systems and optimization and will be divided into two parts: The first part presents an analysis of accelerated first-order optimization algorithms, where the continuous dependence of iterates with respect to their initial conditions will be exploited for characterizing the convergence rate. The result establishes criteria for accelerated convergence of a large class of momentum-based optimization algorithms. The criteria, which are easily verifiable, are necessary and sufficient and therefore precisely characterize optimization algorithms that are accelerated. The analysis applies to non-convex functions, unifies discrete-time and continuous-time models, and rigorously explains why structure-preserving (symplectic) discretization schemes are important in optimization. The second part of the talk introduces a class of first-order methods for constrained optimization that are based on an analogy to non-smooth dynamical systems. The key underlying idea is to express constraints in terms of velocities instead of positions, which has the algorithmic consequence that optimizations over feasible sets at each iteration are replaced with optimizations over local, sparse convex approximations. The result is a simplified suite of algorithms and an expanded range of possible applications in machine learning.


Biographical Information

Michael Muehlebach studied mechanical engineering at ETH Zurich. He received his Ph.D. under the supervision of Prof. R. D'Andrea in 2018 and joined the group of Prof. Michael I. Jordan at the University of California, Berkeley as a postdoctoral researcher. In 2021 he started as an independent group leader at the Max Planck Institute for Intelligent Systems in Tuebingen, where he leads the group "learning and dynamical systems".

He is interested in a variety of subjects, including machine learning, dynamical systems, and optimization. 

He received the Outstanding D-MAVT Bachelor Award for his Bachelor's degree and the Willi-Studer prize for the best Master's degree. His Ph.D. thesis was awarded with the ETH Medal and the HILTI prize for innovative research. He was also awarded a Branco Weiss Fellowship and an Emmy Noether Fellowship, which fund his research group.

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