arXiv:2510.08962v1 Announce Type: cross Abstract: Learning with high-resource data has demonstrated substantial success in artificial intelligence (AI); however, the costs associated with data annotation and model training remain significant. A fundamental objective of AI research is to achieve robust generalization with limited-resource data. This survey employs agnostic active sampling theory within the Probably Approximately Correct (PAC) framework to analyze the generalization error and label complexity associated with learning from low-resource data in both model-agnostic supervised and unsupervised settings. Based on this analysis, we investigate a suite of optimization strategies tailored for low-resource data learning, including gradient-informed optimization, meta-iteration optimization, geometry-aware optimization, and LLMs-powered optimization. Furthermore, we provide a comprehensive overview of multiple learning paradigms that can benefit from low-resource data, including domain transfer, reinforcement feedback, and hierarchical structure modeling. Finally, we conclude our analysis and investigation by summarizing the key findings and highlighting their implications for learning with low-resource data.