Active Sampling of Multiple Sources for Sequential Estimation

Consider $K$ processes, each generating a sequence of identical and independent random variables. The probability measures these processes have parameters that must be estimated. Specifically, they share parameter notation="LaTeX">$\theta$ common to all measures. Additionally, process notation="LaTeX">$i\in \lbrace 1, \dots, K\rbrace$ has private notation="LaTeX">$\alpha _{i}$. objective is design an active sampling algorithm for sequentially estimating in order form reliable estimates shared with the fewest number samples. This three key components: (i) data-driven decisions, which dynamically over time specifies should selected sampling; (ii) stopping process, when accumulated data sufficient terminate process; (iii) estimators parameters. Owing sequential estimation being known analytically intractable, this paper adopts conditional cost functions, leading approach was recently shown render tractable analysis. Asymptotically optimal decision rules (sampling, stopping, estimation) are delineated, numerical experiments provided compare efficacy quality proposed procedure those relevant approaches.