CORMSIS Seminar - Optimisation of multiresolution models Event

Event details

Abstract of the talk: 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, multi scale 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 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.