  Quantifying entanglement for multipartite quantum state is a crucial task in
many aspects of quantum information theory. Among all the entanglement
measures, relative entropy of entanglement $E_{R}$ is an outstanding quantity
due to its clear geometric meaning, easy compatibility with different system
sizes, and various applications in many other related quantity calculations.
Lower bounds of $E_R$ were previously found based on distance to the set of
positive partial transpose states. We propose a method to calculate upper
bounds of $E_R$ based on active learning, a subfield in machine learning, to
generate an approximation of the set of separable states. We apply our method
to calculate $E_R$ for composite systems of various sizes, and compare with the
previous known lower bounds, obtaining promising results. Our method adds a
reliable tool for entanglement measure calculation and deepens our
understanding for the structure of separable states.
