Michael Sedlmayer studied Mathematics at the University of Vienna with a specialization in Applied Mathematics and Scientific Computing. In 2018 he started his PhD position at the research network. His research interests are mainly in the area of nonsmooth optimization. These include theoretical investigations of mathematical optimization problems in both discrete and continuous settings, and the connection to the monotone operator theory in particular. He is interested in the design, development and convergence analysis of numerical algorithms for solving nonsmooth and (potentially) nonconvex optimization problems. On the other hand, he works on using tools and methods from Machine Learning in the domain of Digital Humanities, particularly for digital historical studies. His current focus is to establish methodology for automated classification of ancient Armenian manuscripts.

Dissertation

Convergence Rate Analysis of Optimisation and Minimax Algorithms for Machine Learning

Training machine learning models is done via optimisation algorithms, where due to the typically huge amount of data in most cases so-called “first order” methods are preferred. In my dissertation I develop novel algorithms of this type as well as study and extend already existing ones. To empirically validate all considered methods I provide simple, conceptual problems that showcase the convergence behaviour of the proposed methods. This is complemented by more complex experiments covering relevant real-world machine learning applications, treating, among other things, Generative Adversarial Nets (GANs) and Multikernel Support Vector Machines.

What motivated you to pursue a PhD and how did you choose your field of research?

For my master’s thesis I worked on a project with a big Austrian energy provider, which was my first contact with the field of data science. Besides the very theoretical mathematical contents during my studies, the practical project work was a welcome change. Moreover, the idea of further establishing new knowledge, in particular developing novel mathematical proofs, appeared to be delightful. While I was finishing my master’s, 5 PhD positions at the newly founded Research Network Data Science were announced and I knew that this would be a natural continuation of working at this interface between theory and applications. I was very happy to get the chance to work on a project in the area of “Digital Humanities” (DH), which provided informative insights into a very interesting and rich field.

To what extent was it beneficial for your research to be part of our research network Data Science?

For my work at the interface between theory and applications, it was immensely beneficial to have the opportunity to work with experts in either area. More than once my colleagues at the Research Network were able to provide very helpful input, without which several projects would not have turned out that successful. On a more personal level, sharing offices and coffee breaks with people of various professional backgrounds helped me to get to know the “language” of different fields and how to make my research more accessible to a diverse audience.

What was the most significant discovery of your research and how do you think it will impact your field and benefit our society?

By the nature of (most) research, as improvements or insights tend to be rather incremental, famously described by Newton as “standing on the shoulders of giants” – for me it is very difficult to estimate global impact on the field or even on society. Also, it would be hard to pinpoint a particular project. I am very happy about the consistent work over the last years. We developed novel algorithms, investigated extensions of existing ones, successfully trained GANs and were able to classify ancient Armenian manuscripts by script type, where we saw that this is not only possible but also correct to a substantially high degree.

What were the biggest challenges and how did you maintain your motivation and focus during your studies?

Generally speaking, mathematical research, or knowledge gain in a broader sense, already requires a certain level of frustration tolerance. Sometimes it takes days to find the one correct expression to complete or just to continue a proof. Even though the correct concept for the proof is already there, sometimes seemingly promising approaches lead to nowhere in the end. Concerning the practical work, I would like to address that debugging of code is notoriously tiring. The initial collection of data for the DH project and getting the labels by going through the meta data by hand also needs to be mentioned in this regard.
I think that in general it was helpful that I overall enjoy what I am doing and that I could be certain that after more frustrating phases better times would follow again. I also always had my ultimate goal in mind: writing a doctoral thesis and completing my PhD. In many cases it helped to discuss tricky situations with colleagues to get new ideas or learn from their experience. On the other hand, family and friends were happy to help with diversions to get a fresh mind, and if nothing else helped I could always count on feline support :-)

What are your future career plans and how do you see your PhD degree influencing your professional trajectory?

I think that my PhD at the research network provides a solid foundation for my professional career; be it in academia or in industry. During the last years I learned to cope with rather frustrating and challenging times, and how to tackle problems on my own. To complete these valuable experiences, which in my opinion is even more important, I had the opportunity to work with great colleagues in close collaborations with all its ups and downs. I learned to question all believes – including my own – until they are validated, but to still trust in the knowledge and skills I have acquired along the way.

Please tell us why you stay affiliated to the research network.

I am very grateful to work as a PostDoc researcher in the FFG project “Smart Operation of Wind Turbines under Icing Conditions”, under the lead of Prof. Radu Bot and in collaboration with VERBUND, the Austrian Institute of Technology as well as the Swiss company Meteotest. I will be part of it until the end of its funding period in March 2024. As the project was initially submitted via the Research Network and lies at the interface between practical project work and mathematical research that I mentioned before, this was a most natural choice.