Please Note: This seminar will be given online.
Actuarial Science and Financial Mathematics Seminar Series
Xunyu Zhou, Professor
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.