Designing Optimal Langevin samplers

Greg Pavliotis (Imperial College London)

Friday 30th October, 2015 15:00-16:00 Maths 204


A standard approach to computing expectations with respect to a given probability measure, known up to the normalization constant, is to introduce an appropriate Langevin dynamics that is ergodic with respect to the distribution from which we want to sample. It is by now well understood that breaking detailed balance, i.e. considering nonreversible Langevin dynamics, can speed up convergence to the target distribution and reduce the asymptotic variance. In this talk we will consider a family of underdamped (hypoelliptic) Langevin diffusions that can be used in order to sample from the target distribution. We will address the issue of how we can choose the optimal dynamics, in the sense of minimizing the computational cost. We will also explain how the choice of the optimal dynamics can be combined with appropriate variance reduction techniques. This is joint work with A. Duncan and N. Nusken.


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