Sequential Estimation under Multiple Resources: a Bandit Point of View
This addresses the challenge of efficiently estimating parameters using multiple resources in federated learning, though it is incremental as it builds on bandit theory and statistical estimation.
The paper tackles the problem of Sequential Estimation under Multiple Resources (SEMR) in a federated setting, proposing a lower bound for the fundamental limit and an order-optimal algorithm to achieve it, with performance evaluated by mean squared error and regret based on variance.
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 $θ$. 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.