State-Dependent Temperature Control for Langevin Diffusions
Abstract
We study the temperature control problem for Langevin diffusions in the context of non-convex optimization. The classical optimal control of such a problem is of the bang-bang type, which is overly sensitive to errors. A remedy is to allow the diffusions to explore other temperature values and hence smooth out the bang-bang control. We accomplish this by a stochastic relaxed control formulation incorporating randomization of the temperature control and regularizing its entropy. We derive a state-dependent, truncated exponential distribution, which can be used to sample temperatures in a Langevin algorithm, in terms of the solution to an HJB partial differential equation. We carry out a numerical experiment on a one-dimensional baseline example, in which the HJB equation can be easily solved, to compare the performance of the algorithm with three other available algorithms in search of a global optimum.
Cite
@article{arxiv.2011.07456,
title = {State-Dependent Temperature Control for Langevin Diffusions},
author = {Xuefeng Gao and Zuo Quan Xu and Xun Yu Zhou},
journal= {arXiv preprint arXiv:2011.07456},
year = {2021}
}