Meta-learning, also known as learning to learn, has garnered significant attention in the fields of artificial intelligence and machine learning over the past few years. The core idea of meta-learning is to leverage prior experience and data to enhance quality and efficiency on new tasks. To date, numerous meta-learning algorithms have been studied within continuous domains. Recently, Adibi et al. integrated the concept of meta-learning into submodular optimization for the first time, proposing a discrete meta-learning framework termed submodular meta-learning. This framework can solve a series of tasks \(\varGamma =\{\varGamma _{i}\}\) , where each task \(\varGamma _{i}\) is considered as the problem of maximizing a monotone submodular function \(f_{i}\) under the cardinality constraint (upper bound by k). The goal is to train a common initial set with size l \((0<l<k)\) using prior tasks, which can quickly adapt to new tasks. Through this framework, for each new task, we only need to continue searching for task-specific remaining \((k-l)\) elements based on this common initial set, thereby reducing the computational cost for each new task. Inspired by their work, we investigate a faster algorithm to find this common initial set. We design a fast two-phase algorithm using threshold-decreasing technique, which achieves \((\frac{3}{5}-\frac{1}{5e}-O(\epsilon ))\approx (0.526-O(\epsilon ))\) approximation ratio and optimizes the current query complexity from \(O(mn^{2})\) to \(O(\frac{mn}{\epsilon }\log \frac{n}{\epsilon })\) in the worst case \((k=O(n))\) where n is the size of ground set, m is the number of samples and \(\epsilon \in (0,1)\) is a small constant.
