State-Dependent Temperature Control for Langevin Diffusions

We study the temperature control problem for Langevin diffusions in context of non-convex optimization. The classical optimal such a is bang-bang type, which overly sensitive to errors. A remedy allow explore other values and hence smooth out control. accomplish this by stochastic relaxed formulation incorporating randomization regularizing its entropy. derive state-dependent, truncated exponential distribution, can be used sample temperatures algorithm, terms solution an HJB partial differential equation. carry numerical experiment on one-dimensional baseline example, equation easily solved, compare performance algorithm with three available algorithms search global optimum.