Norkin V.I.
Generalized gradients in dynamic optimization, optimal control, and machine learning problems

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. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: deep learning, dynamic optimization, machine learning, multilayer neural networks, nonsmooth noncovex optimization, optimal control, stochastic generalized gradient, stochastic optimization, stochastic smoothing, Dynamical systems, Multilayer neural networks, Stochastic systems, Discrete dynamical systems, Discrete time, Dynamic optimization, Generalized gradients, Machine learning problem, Neural network learning, Non-smooth dynamics, Optimal controls, Machine learning

Cite:
Norkin V.I. (2020). Generalized gradients in dynamic optimization, optimal control, and machine learning problems. Cybernetics and Systems Analysis, 56 (2), 89–107. doi: https://doi.org/10.1007/s10559-020-00240-x http://jnas.nbuv.gov.ua/article/UJRN-0001103874 [In Russian].