Tail probability estimates of continuous-time simulated annealing processes.

We study the convergence rate of a continuous-time simulated annealing process $ (X_t; \, t \ge 0) $ for approximating the global optimum of a given function $ f $. We prove that the tail probability $ \mathbb{P}(f(X_t) > \min f +\delta) $ decays polynomial in time with an appropriately chosen cooling schedule of temperature, and provide an explicit convergence rate through a non-asymptotic bound. Our argument applies recent development of the Eyring-Kramers law on functional inequalities for the Gibbs measure at low temperatures. [ABSTRACT FROM AUTHOR]