Pelletier, Mariane, Weak convergence rates for stochastic approximation with application to multiple targets and simulated annealing, Annals of applied probability , 8(1), 1998, pp. 10-44
We study convergence rates of R-valued algorithms, especially in the case of multiple targets and simulated annealing. We precise, for example, the convergence rate of simulated annealing algorithms, whose weak convergence to a distribution concentrated on the potential's minima had been established by Gelfand and Mitter or by Hwang and Sheu.