The challenge of delivering efficient explanations is a critical barrier that prevents the adoption of model explanations in real-world applications. Existing approaches often depend on extensive model queries for sample-level explanations or rely on expert's knowledge of specific model structures that trade general applicability for efficiency. To address these limitations, this paper introduces a novel framework Fast EXplanation (FEX) that represents attribution-based explanations via probability distributions, which are optimized by leveraging the policy gradient method. The proposed framework offers a robust, scalable solution for real-time, large-scale model explanations, bridging the gap between efficiency and applicability. We validate our framework on image and text classification tasks and the experiments demonstrate that our method reduces inference time by over 97 percent and memory usage by 70 percent compared to traditional model-agnostic approaches while maintaining high-quality explanations and broad applicability.