Temperature Control for Langevin Diffusions
Team Information
Team Members
Xunyu Zhou, Liu Family Professor of Financial Engineering, Industrial Engineering and Operations Research, School of Engineering and Applied Science, Columbia University
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 any 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. We carry out a numerical experiment to compare the performance of the algorithm with two other available algorithms in search of a global optimum.
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Team Contact: Xunyu Zhou (use form to send email)
