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Multiresolution Optimisation Algorithms: Theory and Applications

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Abstract:
Multiresolution optimisation algorithms are applicable when the underlying optimisation model can be modelled using varying levels of fidelity. Typical examples include optimisation of systems governed by differential equations in computer vision and optimal control, the number of features in machine learning applications, the number of states in a Markov Decision Processes, and so on. Indeed anytime a finite dimensional optimisation model arises from an infinite dimensional model it is straightforward to define such a hierarchy of optimisation models.

In this talk we discuss how to take advantage of the availability of a hierarchy of models in a consistent manner. We posit that when the so called approximation property does not hold then the best one can hope for is to match the complexity of the single resolution algorithm. However, when additional assumptions can be made about the relationship between the coarse and fine models it is possible to improve the complexity of the optimisation algorithm. We illustrate our points by developing a multiresolution proximal point algorithm for non-smooth optimisation and a multiresolution value iteration algorithm for Markov Decision Processes. We establish the worst case complexity of the proposed methods and compare them with the state-of-the-art in terms of theoretical convergence guarantees and numerical performance.

Type of Seminar:
Optimization and Applications Seminar
Speaker:
Dr. Panos Parpas
Department of Computing at Imperial College London
Date/Time:
Mar 30, 2015   16:30
Location:

HG G 19.1, Rämistrasse 101
Contact Person:

Prof. Lygeros
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Biographical Sketch:
Panos Parpas is a Lecturer in the Computational Optimization Group of the Department of Computing at Imperial College London. He is also a member of the Centre for Process Systems Engineering at Imperial College London. Before that, he was a postdoctoral associate in the Energy Systems Division of the Massachusetts Institute of Technology (2009–2011). Dr. Parpas is interested in the development of computational optimization methods. He is particularly interested in multiresolution algorithms for global optimization and decision making under uncertainty.