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

Vladimir Norkin (vladimir.norkin***at***gmail.com)

Abstract: In this work, nonconvex nonsmooth problems of dynamic optimization, optimal control in discrete time (including feedback control), and machine learning are considered from a common point of view. An analogy is observed between tasks of controlling discrete dynamic systems and training multilayer neural networks with nonsmooth target function and connections. Methods for calculating generalized gradients for such systems based on Hamilton-Pontryagin functions are substantiated. Stochastic generalized gradient algorithms are extended for optimal controlling and learning nonconvex nonsmooth dynamic systems.

Keywords: dynamic optimization, optimal control, machine learning, multilayer neural networks, deep learning, nonconvex nonsmooth optimization, stochastic optimization, stochastic generalized gradient

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Stochastic Programming

Citation: V.M. Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine, Kiev, 18 September, 2019. To appear in "Cybernatics and Systems Analysis".

Download: [PDF]

Entry Submitted: 09/18/2019
Entry Accepted: 09/18/2019
Entry Last Modified: 10/10/2019

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