The purpose of this paper is to find asymptotically optimal Bayes sequential procedures for estimating a function $g(\theta_1, \theta_2,\cdots, \theta_k)$ when there are $k$ experiments $E_1, E_2,\cdots, E_k$ and the performance of the experiment $E_i$ conducts to the observation of a random variable whose distribution depends on the vector parameter $\theta_i$. The term asymptotical refers here to the cost of experimentation tending to zero. The methods used are a generalization of those introduced by Bickel and Yahav.
"Asymptotically Optimal Bayes Sequential Design of Experiments for Estimation." Ann. Statist. 1 (5) 822 - 837, September, 1973. https://doi.org/10.1214/aos/1176342504