I have read the original paper of dynamically weighted IS. However, I do not understand why is the ordinary IS is unbiased, but the dynamically weighted IS is biased.
From the paper, it can be proven that the expectation of importance sampling is the same as the expectation of the target function $h(x)$ as the below equation.
$$
E(h(x))=\frac{\Sigma h\left(x_{i}\right) w_{i}}{\Sigma w_{i}}
$$
Therefore, why is the dynamically weighted importance sampling(IS) biased?
References: Wong, Wing Hung, and Faming Liang. "Dynamic weighting in Monte Carlo and optimization." Proceedings of the National Academy of Sciences 94.26 (1997): 14220-14224.