'Institute of Electrical and Electronics Engineers (IEEE)'
Doi
Abstract
In this paper, we study the mixing time of Markov Chain Monte Carlo (MCMC) for integer least-square (LS) optimization problems. It is found that the mixing time of
MCMC for integer LS problems depends on the structure of the underlying lattice. More specifically, the mixing time of MCMC is closely related to whether there is a local minimum in the lattice structure. For some lattices, the mixing time
of the Markov chain is independent of the signal-to-noise ratio (SNR) and grows polynomially in the problem dimension; while for some lattices, the mixing time grows unboundedly as SNR grows. Both theoretical and empirical results suggest
that to ensure fast mixing, the temperature for MCMC should often grow positively as the
SNR increases. We also derive the probability that there exist local minima in an integer least-square problem, which can be as high as 1/3 - 1/√5 + (2 arctan(√(5/3))/(√5Π)