July 17 – 22 , 2011, Dagstuhl Seminar 11291

Mathematical and Computational Foundations of Learning Theory


Matthias Hein (Universität des Saarlandes, DE)
Gabor Lugosi (UPF – Barcelona, ES)
Lorenzo Rosasco (MIT – Cambridge, US)
Stephen Smale (City University – Hong Kong, HK)

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Dagstuhl Service Team


Dagstuhl Report, Volume 1, Issue 7 Dagstuhl Report
List of Participants
Dagstuhl Seminar Schedule [pdf]


The study of learning is at the very core of the problem of intelligence both in humans and machines. We have witnessed an exciting success story of machine learning in recent years.

Among other examples, we now have cars that detect pedestrians, and smart-phones that can be controlled simply by our voices. Indeed, aside from the increase in computational power and availability of large amount of data, the key to these successes has been the development of efficient learning algorithms based on solid theoretical foundations. As the science and engineering of learning move forward to understand and solve richer and more articulated classes of problems, broadening the mathematical and computational foundations of learning becomes essential for future achievements.

The main goal of our seminar was to account for the newest developments in the field of learning theory and machine learning as well as to indicate challenges for the future. This seminar was in the same spirit of two very successful conferences titled `Mathematical Foundations of Learning Theory'', organized in 2004 in Barcelona and 2006 in Paris. The seminar brought together leading researchers from computer science and mathematics to discuss the state of the art in learning and generate synergy effects between the different usually disconnected communities. This Dagstuhl seminar has been the first to cover the full range of facets of modern learning theory.

The seminar has focused on three main topics, while trying to keep a broader view on all recent advances. The three main topics were: 1) the role of sparsity in learning, 2) the role of geometry in learning, and 3) sequential learning and game theory. Experts in each field gave tutorials on each topic, covering basic concepts as well as recent results.

The meeting was hold in a very informal and stimulating atmosphere. The participants all agreed that such a seminar should be come a regular meeting.


We thank Annette Beyer and Claudia Thiele for their continuous support and help in organizing this workshop. Moreover, we would like to thank the staff at Schloss Dagstuhl for making this seminar such a remarkably enjoyable event. Special thanks go to Elisabeth Chaverdian for her wonderful piano concert with excerpts from her current program of the works of Liszt.

Related Dagstuhl Seminar


  • Artificial Intelligence
  • Algorithms
  • Optimization


  • Learning theory
  • Machine learning
  • Sparsity
  • High-dimensional geometry
  • Manifold learning
  • Online learning
  • Reinforcement learning


In the series Dagstuhl Reports each Dagstuhl Seminar and Dagstuhl Perspectives Workshop is documented. The seminar organizers, in cooperation with the collector, prepare a report that includes contributions from the participants' talks together with a summary of the seminar.


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Dagstuhl's Impact

Please inform us when a publication was published as a result from your seminar. These publications are listed in the category Dagstuhl's Impact and are presented on a special shelf on the ground floor of the library.


Furthermore, a comprehensive peer-reviewed collection of research papers can be published in the series Dagstuhl Follow-Ups.