Blip Up-Down Acquisition (BUDA) has been successful in generating distortion-free multi-shot EPI (msEPI) without navigators, utilizing a fieldmap and structured low-rank constraints. Recently, a scan-specific artificial neural network (ANN) motivated by structured low-rank modeling, named LORAKI, has been proposed for refined MRI reconstruction, where its training employed fully-sampled autocalibrated signal (ACS). Although applying LORAKI framework to BUDA is beneficial, acquiring fully-sampled ACS for msEPI is not practical. We propose scan-specific unsupervised ANNs for improved BUDA msEPI without training data. Experiment results indicate that the proposed BUDA-LORAKI exhibits advantages, with up to 1.5x reduction in NRMSE compared to standard BUDA reconstruction.