Neural approximators for functional optimization
R. Zoppoli, Thomas Parisini, Marcello Sanguineti · 2002
Functional optimization problems can be solved analytically only if special assumptions are verified. The approximation method that we propose for the general case is based on the following steps: 1) the decision law is constrained to assume a fixed structure, in which a certain number of free parameters must be optimized, and this enables the functional optimization problem to be reduced to a nonlinear programming one; 2) as a fixed structure, we choose, among various nonlinear approximators, the input/output mapping of multilayer feedforward neural networks; and 3) the resulting nonlinear programming problem is characterized by a highly complex cost function. We propose to minimize it by stochastic programming algorithms. As test-beds for the solving technique, we address a stochastic optimal control problem and an estimation problem, whose solutions are traditionally regarded as difficult tasks.