The subject disclosure pertains to systems and methods for training machine learning systems. Many cost functions are not smooth or differentiable and cannot easily be used during training of a machine learning system. The machine learning system can include a set of estimated gradients based at least in part upon the ranked or sorted results generated by the learning system. The estimated gradients can be selected to reflect the requirements of a cost function and utilized instead of the cost function to determine or modify the parameters of the learning system during training of the learning system.