Adaptive Estimation of Random Vectors with Bandit Feedback

03/31/2022
by   Dipayan Sen, et al.
0

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. This reduces to learning an optimal subset for estimating the entire vector. Towards this, we first establish an exponential concentration bound for an estimate of the MSE for each observable subset. We then frame the estimation problem with bandit feedback in the best-subset identification setting. We propose a variant of the successive elimination algorithm to cater to the adaptive estimation problem, and we derive an upper bound on the sample complexity of this algorithm. In addition, to understand the fundamental limit on the sample complexity of this adaptive estimation bandit problem, we derive a minimax lower bound.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

02/08/2019

Correlated bandits or: How to minimize mean-squared error online

While the objective in traditional multi-armed bandit problems is to fin...
01/10/2019

Mean Estimation from One-Bit Measurements

We consider the problem of estimating the mean of a symmetric log-concav...
06/02/2022

Dynamic Structure Estimation from Bandit Feedback

This work present novel method for structure estimation of an underlying...
09/29/2021

Sequential Estimation under Multiple Resources: a Bandit Point of View

The problem of Sequential Estimation under Multiple Resources (SEMR) is ...
02/06/2022

Missing Mass Estimation from Sticky Channels

Distribution estimation under error-prone or non-ideal sampling modelled...
02/09/2022

Optimal Clustering with Bandit Feedback

This paper considers the problem of online clustering with bandit feedba...
12/03/2017

Iterative Collaborative Filtering for Sparse Matrix Estimation

The sparse matrix estimation problem consists of estimating the distribu...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.