Recent advances in high-power, high-repetition-rate laser systems are driving the adoption of data-driven experimental approaches in high-energy density science. To fully realize the potential of these methodologies, automated and high-throughput analysis of key diagnostics is essential for effective feedback and real-time optimization. We present a novel algorithm, ARISE (algorithm for rapid ion spectrum extraction), developed for fast and reliable extraction of laser-accelerated ion spectra from Thomson parabola spectrometers, capable of operating at repetition rates exceeding 20 Hz. ARISE enables real-time, data-driven experimentation through features including background subtraction, automatic identification of the zero-deflection reference point and automated determination of maximum ion energy. We validate the accuracy of ARISE in spectrum extraction and energy detection, and demonstrate its integration within a Bayesian optimization framework during a proof-of-concept experiment conducted using the 350 TW SCAPA laser, enabling real-time optimization of laser-accelerated ion beam parameters.