Properties and limitations of geometric tempering for gradient flow dynamics

TMLR Paper7462 Authors

Abstract:

We consider the problem of sampling from a probability distribution $\pi$. It is well known that this can be written as an optimisation problem over the space of probability distributions in which we aim to minimise the Kullback--Leibler divergence from $\pi$.
We consider the effect of replacing $\pi$ with a sequence of moving targets $(\pi_t)_{t\ge0}$ defined via geometric tempering on the Wasserstein and Fisher--Rao gradient flows.
We show that replacing the target distribution with a geometric mixture of initial and target distribution does not lead to a convergence speed up.

Submission Type: Regular submission (no more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=DfiHvr2Z8X&noteId=Jj4tX8hPoO

Changes Since Last Submission: Removed acknowledgements for double blind policy.

Assigned Action Editor: ~Trevor_Campbell1

Submission Number: 7462