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SUMMARY:Learning-Rate-Free Optimisation on the Space of Probability Measur
 es - Louis Sharrock (University College London)
DTSTART:20250626T130000Z
DTEND:20250626T140000Z
UID:TALK232318@talks.cam.ac.uk
DESCRIPTION:The task of sampling from a target probability distribution wh
 ose density is only known up to a normalisation constant is of fundamental
  importance to computational statistics and machine learning. There are va
 rious popular approaches to this task\, including Markov chain Monte Carlo
  (MCMC) and variational inference (VI). More recently\, there has been gro
 wing interest in developing hybrid sampling methods which combine the non-
 parametric nature of MCMC with the parametric approach used in VI. In part
 icular\, particle based variational inference (ParVI) methods approximate 
 the target distribution using an ensemble of interacting particles\, which
  are deterministically updated by iteratively minimising a metric such as 
 the Kullback-Leibler divergence. Unfortunately\, such methods invariably d
 epend on hyperparameters such as the learning rate\, which must be careful
 ly tuned by practitioners in order to ensure convergence to the target dis
 tribution at a suitable rate.\nIn this talk\, we introduce a suite of new 
 sampling algorithms which are entirely learning rate free. Our approach le
 verages the perspective of sampling as an optimisation problem over the sp
 ace of probability measures\, and existing ideas from convex optimisation.
  We discuss how to establish the convergence of our algorithms under assum
 ptions on the target distribution. We then illustrate the performance of o
 ur approach on a range of numerical examples\, including several high dime
 nsional models and datasets\, demonstrating comparable performance to exis
 ting state-of-the-art sampling algorithms\, but with no need to tune a lea
 rning rate. Finally\, we discuss how our approach can be adapted for two r
 elated problems: (i) sampling on constrained domains and (ii) inference an
 d learning in latent variable models.&nbsp\;&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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