# Sequential Estimation under Multiple Resources: a Bandit Point of View

arXiv: https://arxiv.org/abs/2109.14703 · HTML: https://mlsanity.com/paper/2109.14703/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 23 references that are in the map.
- First posted on arXiv 29 Sep 2021.

## Builds on (most cited first, 10 of 10)

- [Communication Lower Bounds for Statistical Estimation Problems via a Distributed Data Processing Inequality](https://mlsanity.com/paper/1506.07216/) (2015)
- [Challenges of Big Data Analysis](https://mlsanity.com/paper/1308.1479/) (2013)
- [Adaptive Exploration in Linear Contextual Bandit](https://mlsanity.com/paper/1910.06996/) (2019)
- [Geometric Lower Bounds for Distributed Parameter Estimation under Communication Constraints](https://mlsanity.com/paper/1802.08417/) (2018)
- [On Communication Cost of Distributed Statistical Estimation and Dimensionality](https://mlsanity.com/paper/1405.1665/) (2014)
- [Fisher information under local differential privacy](https://mlsanity.com/paper/2005.10783/) (2020)
- [Statistical Inference for Online Decision-Making: In a Contextual Bandit Setting](https://mlsanity.com/paper/2010.07283/) (2020)
- [Interactive Inference under Information Constraints](https://mlsanity.com/paper/2007.10976/) (2020)
- [Online Variance Reduction for Stochastic Optimization](https://mlsanity.com/paper/1802.04715/) (2018)
- [Statistical Inference, Learning and Models in Big Data](https://mlsanity.com/paper/1509.02900/) (2015)

## Built on by (most cited first, 1 of 1)

- [On Collaboration in Distributed Parameter Estimation with Resource Constraints](https://mlsanity.com/paper/2307.06442/) (2023)

## Abstract (arXiv)

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.