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2020

State-Dependent Temperature Control for Langevin Diffusions

Gao, Xuefeng, Xu, Zuo Quan, Zhou, Xun Yu

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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.

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