# Minimum mean-squared error estimation with bandit feedback

arXiv: https://arxiv.org/abs/2203.16810 · HTML: https://mlsanity.com/paper/2203.16810/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 20 references that are in the map.
- First posted on arXiv 31 Mar 2022.

## Builds on (most cited first, 4 of 4)

- [On the Complexity of Best Arm Identification in Multi-Armed Bandit Models](https://mlsanity.com/paper/1407.4443/) (2014)
- [Correlated Multi-armed Bandits with a Latent Random Source](https://mlsanity.com/paper/1808.05904/) (2018)
- [Most Correlated Arms Identification](https://mlsanity.com/paper/1404.5903/) (2014)
- [Correlated bandits or: How to minimize mean-squared error online](https://mlsanity.com/paper/1902.02953/) (2019)

## Abstract (arXiv)

We consider the problem of sequentially learning to estimate, in the mean squared error (MSE) sense, a Gaussian K-vector of unknown covariance by observing only m < K of its entries in each round. We propose two MSE estimators, and analyze their concentration properties. The first estimator is non-adaptive, as it is tied to a predetermined m-subset and lacks the flexibility to transition to alternative subsets. The second estimator, which is derived using a regression framework, is adaptive and exhibits better concentration bounds in comparison to the first estimator. We frame the MSE estimation problem with bandit feedback, where the objective is to find the MSE-optimal subset with high confidence. We propose a variant of the successive elimination algorithm to solve this problem. We also derive a minimax lower bound to understand the fundamental limit on the sample complexity of this problem.