We develop a stochastic algorithm for independent component analysis that incorporates multi-trial supervision, which is available in many scientific contexts. The method blends a proximal gradient-type algorithm in the space of invertible matrices with joint learning of a prediction model through backpropagation. We illustrate the proposed algorithm on synthetic and real data experiments. In particular, owing to the additional supervision, we observe an increased success rate of the non-convex optimization and the improved interpretability of the independent components.