Reliable Integration of Continuous Constraints Into Extreme Learning Machines

The application of machine learning methods in the engineering of intelligent technical systems often requires the integration of continuous constraints like positivity, monotonicity, or bounded curvature in the learned function to guarantee a reliable performance. We show that the extreme learning machine is particularly well suited for this task. Constraints involving arbitrary derivatives of the learned function are effectively implemented through quadratic optimization because the learned function is linear in its parameters, and derivatives can be derived analytically. We further provide a constructive approach to verify that discretely sampled constraints are generalized to continuous regions and show how local violations of the constraint can be rectified by iterative re-learning. We demonstrate the approach on a practical and challenging control problem from robotics, illustrating also how the proposed method enables learning from few data samples if additional prior knowledge about the problem is available.