# Active Sampling of Multiple Sources for Sequential Estimation

arXiv: https://arxiv.org/abs/2208.05406 · HTML: https://mlsanity.com/paper/2208.05406/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 57 references that are in the map.
- First posted on arXiv 10 Aug 2022.

## Builds on (most cited first, 7 of 7)

- [Optimal Best Arm Identification with Fixed Confidence](https://mlsanity.com/paper/1602.04589/) (2016)
- [Improving the Expected Improvement Algorithm](https://mlsanity.com/paper/1705.10033/) (2017)
- [Fixed-Confidence Guarantees for Bayesian Best-Arm Identification](https://mlsanity.com/paper/1910.10945/) (2019)
- [Controlled Sensing for Sequential Multihypothesis Testing with Controlled Markovian Observations and Non-Uniform Control Cost](https://mlsanity.com/paper/1310.1844/) (2013)
- [Active Classification for POMDPs: a Kalman-like State Estimator](https://mlsanity.com/paper/1312.2039/) (2013)
- [Optimal Index Policies for Anomaly Localization in Resource-Constrained Cyber Systems](https://mlsanity.com/paper/1405.4098/) (2014)
- [Distributed Chernoff Test: Optimal decision systems over networks](https://mlsanity.com/paper/1809.04587/) (2018)

## Built on by (most cited first, 2 of 2)

- [Evasive Active Hypothesis Testing with Deep Neuroevolution: The Single- and Multi-Agent Cases](https://mlsanity.com/paper/2403.10112/) (2024)
- [Searching for a Hidden Markov Anomaly over Multiple Processes](https://mlsanity.com/paper/2506.17108/) (2025)

## Abstract (arXiv)

Consider K processes, each generating a sequence of identical and independent random variables. The probability measures of these processes have random parameters that must be estimated. Specifically, they share a parameter θ common to all probability measures. Additionally, each process i∈1, dots, K has a private parameter αi. The objective is to design an active sampling algorithm for sequentially estimating these parameters in order to form reliable estimates for all shared and private parameters with the fewest number of samples. This sampling algorithm has three key components: (i)~data-driven sampling decisions, which dynamically over time specifies which of the K processes should be selected for sampling; (ii)~stopping time for the process, which specifies when the accumulated data is sufficient to form reliable estimates and terminate the sampling process; and (iii)~estimators for all shared and private parameters. Owing to the sequential estimation being known to be analytically intractable, this paper adopts emph conditional estimation cost functions, leading to a sequential estimation approach that was recently shown to render tractable analysis. Asymptotically optimal decision rules (sampling, stopping, and estimation) are delineated, and numerical experiments are provided to compare the efficacy and quality of the proposed procedure with those of the relevant approaches.