Generalized Gradients in Dynamic Optimization, Optimal Control, and Machine Learning Problems*

Abstract

Problems of nonsmooth nonconvex dynamic optimization, optimal control (in discrete time), including feedback control, and machine learning are considered from a common point of view. An analogy between controlling discrete dynamical systems and multilayer neural network learning problems with nonsmooth objective functionals and connections is traced. Methods for computing generalized gradients for such systems based on the Hamilton–Pontryagin functions are developed. Gradient (stochastic) algorithms for optimal control and learning are extended to nonconvex nonsmooth dynamic systems.