Neural approximations in discounted infinite-horizon stochastic optimal control problems. (September 2018)

• Record Type: Journal Article
• Authors: Gnecco, Giorgio; Sanguineti, Marcello
• Is Part Of: Engineering applications of artificial intelligence. Volume 74(2018)
• Page Start: 294
• Page End: 302
• Publication Date: 2018-09
• Subjects: Stochastic optimal control -- Infinite horizon with discount -- Optimal stationary closed-loop control -- Neural networks -- Approximation; Engineering -- Data processing -- Periodicals; Artificial intelligence -- Periodicals; Expert systems (Computer science) -- Periodicals; Ingénierie -- Informatique -- Périodiques; Intelligence artificielle -- Périodiques; Systèmes experts (Informatique) -- Périodiques; Artificial intelligence; Engineering -- Data processing; Expert systems (Computer science); Periodicals; 620.00285
• DOI: 10.1016/j.engappai.2018.07.004
• Languages: English
• ISSNs: 0952-1976

Abstract

Abstract: Neural approximations of the optimal stationary closed-loop control strategies for discounted infinite-horizon stochastic optimal control problems are investigated. It is shown that for a family of such problems, the minimal number of network parameters needed to achieve a desired accuracy of the approximate solution does not grow exponentially with the number of state variables. In such a way, neural-network approximation mitigates the so-called "curse of dimensionality". The obtained theoretical results point out the potentialities of neural-network based approximation in the framework of sequential decision problems with continuous state, control, and disturbance spaces.