Let $f:A \to R$ be a bounded continuous function with global minimum $f(a)=0$ and let $X_t:\Omega\to A$ be a discrete time stochastic process which converges in probability to $a$. Asymptotic convergence rate (ACR) is a measure of convergence rate given by ${\rm ACR}=\limsup_t (E[f(X_t)] )^{1/t}$, where $E[.]$ denotes the expected value. Equivalently: $\log({\rm ACR})=\limsup_t (1/t) \cdot \log(E[f(X_t)])$. We will talk about ACR in finite-dimensional case ($A$ is a subset of $R^d$). The motivation behind presented results is convergence of evolutionary algorithms.
Identyfikator: 251 152 4038 Kod: 276466