Web: http://arxiv.org/abs/2010.11176

Sept. 15, 2022, 1:12 a.m. | Mufan Bill Li, Murat A. Erdogdu

stat.ML updates on arXiv.org arxiv.org

We propose a Langevin diffusion-based algorithm for non-convex optimization
and sampling on a product manifold of spheres. Under a logarithmic Sobolev
inequality, we establish a guarantee for finite iteration convergence to the
Gibbs distribution in terms of Kullback--Leibler divergence. We show that with
an appropriate temperature choice, the suboptimality gap to the global minimum
is guaranteed to be arbitrarily small with high probability.

As an application, we consider the Burer--Monteiro approach for solving a
semidefinite program (SDP) with diagonal constraints, …

algorithm arxiv

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