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Please join us for a CCN/CCM Seminar with Mario Lezcano-Casado, doctoral candidate in the Mathematical Institute, University of Oxford, for the following talk:
Title: Optimisation on Manifolds: Theory and practice
Abstract: In this talk, we will present an approach to constrained optimisation when the set of constraints is a smooth manifold. This setting is of particular interest in data science applications, as many interesting sets of matrices have a manifold structure. We will show how we may couple classic ideas from differential geometry with modern applied methods such as autodifferentiation to simplify optimisation problems from spaces with a difficult topology (e.g. problems with orthogonal, positive definite, or fixed-rank constraints) to problems on ℝⁿ where we can use any classical optimisation methods to attack them. We will also show how to use these methods to automatically compute quantities such as the Riemannian gradient and the Hessian. We will present the library GeoTorch that allows for putting these kind of constraints within models written in PyTorch without modifying the model itself. We will also comment on some convergence results if time allows.