Pseudo-inverse learners (PILs) are a kind of feedforward neural network trained with the pseudoinverse learning algorithm, which can be traced back to 1995 originally. PIL is an approach for nongradient descent learning, and its main advantage is the lower computational cost and fast learning procedure, which is especially relevant in the edge computing research field. However, PIL is mostly applied to a deterministic learning problem, while in the real world, the greatest case that is of concern is the uncertainty learning problem. In this work, under the framework of the synergetic learning system (SLS), we introduce an approximated synergetic learning scheme, which can transform uncertainty learning into deterministic learning. We call this new learning framework the Bayesian PIL, and the advantages are also demonstrated in this work.