A Theoretical Framework for End-to-End Learning of Deep Neural Networks With Applications to Robotics

Deep Learning (DL) systems are difficult to analyze and proving convergence of DL algorithms like backpropagation is an extremely challenging task as it is a highly non-convex and high-dimensional problem. When using DL algorithms in robotic systems, theoretical analysis of stability, convergence, and robustness is a vital procedure as robots need to operate in a predictable manner to ensure safety. This paper presents the first unified End-to-End (E2E) learning framework that can be applied to both classification problems and real-time kinematic robot control tasks. In the proposed forward simultaneous learning method, the weights of all layers of the fully connected neural networks are updated concurrently. The proposed E2E learning framework uses an adjustable ReLU activation function so that convergence of the output error to a bound, which is dependent on the neural network approximation error, can be ensured. In particular, it is shown that the error between ideal output and estimated output of the network can converge to and stay in a certain bound, and this bound reduces to zero when the approximation error is zero. Therefore, the robustness of the learning system can be ensured even in the presence of the approximation error. Two case studies are done on classification tasks using MNIST and CIFAR10 datasets by using the proposed learning method, and the results show that the E2E learning method achieves comparable test accuracy as the gradient descent method and the main advantage is that convergence can be ensured during training. The framework is also implemented on a UR5e robot with unknown kinematic model, which is the first result on real-time E2E learning of deep neural networks for kinematic control of robots with guaranteed convergence.