Gaussian Cooling and Dikin Walks: The Interior-Point Method for Logconcave Sampling

arXiv:2307.12943v4 Announce Type: replace-cross
Abstract: The connections between (convex) optimization and (logconcave) sampling have been considerably enriched in the past decade with many conceptual and mathematical analogies. For instance, the Langevin algorithm can be viewed as a sampling analogue of gradient descent and has condition-number-dependent guarantees on its performance. In the early 1990s, Nesterov and Nemirovski developed the Interior-Point Method (IPM) for convex optimization based on self-concordant barriers, providing efficient algorithms for structured convex optimization, often faster than the general …

abstract algorithm arxiv cooling cs.ds cs.lg gradient instance math.oc optimization performance sampling type