  The problem of Sequential Estimation under Multiple Resources (SEMR) is
defined in a federated setting. SEMR could be considered as the intersection of
statistical estimation and bandit theory. In this problem, an agent is
confronting with k resources to estimate a parameter $\theta$. The agent should
continuously learn the quality of the resources by wisely choosing them and at
the end, proposes an estimator based on the collected data. In this paper, we
assume that the resources' distributions are Gaussian. The quality of the final
estimator is evaluated by its mean squared error. Also, we restrict our class
of estimators to unbiased estimators in order to define a meaningful notion of
regret. The regret measures the performance of the agent by the variance of the
final estimator in comparison to the optimal variance. We propose a lower bound
to determine the fundamental limit of the setting even in the case that the
distributions are not Gaussian. Also, we offer an order-optimal algorithm to
achieve this lower bound.
