\section{Related Works}
\label{sec:related_works}

The quest to minimize data annotation costs has sparked a wave of research aimed at creating innovative approaches and algorithms for crowdsourcing tasks.

A significant line of work focuses on optimizing instance selection strategies for querying worker labels, often under the assumption of a uniform labeling cost. Among these studies, \citep{zhou2014optimal} explores non-sequential instance selection, employing aggregate regret to identify the top $K$ arms with the highest expected rewards in a stochastic $n$-armed bandit framework. In contrast, several studies~\citep{sheng2008get, li2016crowdsourcing, frazier2008knowledge, chen2013optimistic, raykar2014sequential} focus on sequential instance selection with varying objectives. For instance, \citep{sheng2008get} and \citep{li2016crowdsourcing} aim to maximize the number of labeled instances while adhering to quality requirements and budget constraints. While \citep{sheng2008get} assumes uniform data labeling quality across instances, \citep{li2016crowdsourcing} posits that easier instances yield higher-quality labels. \citep{raykar2014sequential} seeks to maximize a utility function that accounts for a pull market, where workers may choose to decline jobs from requesters. In a similar vein, \citep{frazier2008knowledge} and~\citep{chen2013optimistic} aim to enhance labeling accuracy within budget limits. The former proposes a knowledge gradient policy for sequential instance selection, while the latter critiques this policy's consistency, introducing an optimistic variant that proves consistent under infinite budget scenarios.

However, these studies often treat instances as independent and identically distributed (i.i.d.), neglecting potential correlations between them. Related to our work, \citep{pmlr-v216-kulkarni23a} does consider instance correlations and strives to maximize overall labeling accuracy within budget constraints. Nonetheless, they rely on the assumption that these correlations are predetermined, a stance that may be problematic, particularly in non-homogeneous graphs. In this work, we make significant advancements by relaxing previous assumptions and dynamically estimating instance correlations as labels are obtained in real time. Given that workers do not provide instance correlations, we introduce a novel entropy-based objective function that minimizes uncertainty in both instance labeling and correlation estimation. Notably, we are the first to estimate instance correlations and leverage this information for budget allocation, effectively reducing data labeling costs. This innovative approach marks a key contribution to the field, enhancing both the accuracy and efficiency of online data labeling processes.