Simulated annealing from continuum to discretization: a convergence analysis via the Eyring--Kramers law
We study the convergence rate of continuous-time simulated annealing $(X_t; \, t \ge 0)$ and its discretization $(x_k; \, k =0,1, \ldots)$ for approximating the global optimum of a given function $f$. We prove that the tail probability $\mathbb{P}(f(X_t) > \min f +\delta)$ (resp. $\mathbb{P}(f(x_k) > \min f +\delta)$) decays polynomial in time (resp. in cumulative step size), and provide an explicit rate as a function of the model parameters. Our argument applies the recent development on functional inequalities for the Gibbs measure at low temperatures -- the Eyring-Kramers law. In the discrete setting, we obtain a condition on the step size to ensure the convergence.
PDF AbstractTasks
Datasets
Add Datasets
introduced or used in this paper
Results from the Paper
Submit
results from this paper
to get state-of-the-art GitHub badges and help the
community compare results to other papers.
Methods
No methods listed for this paper. Add
relevant methods here
