In the context of learning and inference for non-Gaussian additive noise processes, several non-Bussgang learning criteria have emerged, such as, the maximum correntropy, minimum error entropy, and the maximum Versoria criterion. However, these existing learning criteria are known to depend on hyperparameters such as the shape and the spread parameters, which make these approaches susceptible to arbitrary hyperparameter choices. This work proposes an online hyperparameter free criterion learning algorithm that comprehensively alleviates dependence on hyperparameter choices and self-adapts to underlying noise distributions. For the proposed hyperparameter-free criterion learning, analytical results are derived, and case-studies are presented for its validation.