Department Seminar by Xunyu Zhou

Friday, December 4, 2020 10:30 am - 10:30 am EST (GMT -05:00)

Please Note: This seminar will be given online.

Actuarial Science and Financial Mathematics Seminar Series

Xunyu Zhou, Professor
Columbia University 

Link to join seminar: Hosted on Webex.

Temperature Control for Langevin Diffusions

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.