  Data constitute the foundational component of the data economy and its
marketplaces. Efficient and fair data valuation has emerged as a topic of
significant interest.\ Many approaches based on marginal contribution have
shown promising results in various downstream tasks. However, they are well
known to be computationally expensive as they require training a large number
of utility functions, which are used to evaluate the usefulness or value of a
given dataset for a specific purpose. As a result, it has been recognized as
infeasible to apply these methods to a data marketplace involving large-scale
datasets. Consequently, a critical issue arises: how can the re-training of the
utility function be avoided? To address this issue, we propose a novel data
valuation method from the perspective of optimal control, named the neural
dynamic data valuation (NDDV). Our method has solid theoretical interpretations
to accurately identify the data valuation via the sensitivity of the data
optimal control state. In addition, we implement a data re-weighting strategy
to capture the unique features of data points, ensuring fairness through the
interaction between data points and the mean-field states. Notably, our method
requires only training once to estimate the value of all data points,
significantly improving the computational efficiency. We conduct comprehensive
experiments using different datasets and tasks. The results demonstrate that
the proposed NDDV method outperforms the existing state-of-the-art data
valuation methods in accurately identifying data points with either high or low
values and is more computationally efficient.
