Neural Approximations for Optimal Control and Decision

Many areas of science and technology require the solution of functional optimization problems, that is, problems with feasible solutions belonging to infinite-dimensional spaces. This is the case, for example in stochastic optimal control of communication or traffic networks: large organizations in which many individual decision makers, each with different information available cooperate for the accomplishment of a common goal. In such circumstances, there is often a variety of technical impediments to the use of traditional optimal control tools - strong nonlinearity, non-Gaussian noise, multiple decision makers, "e;Bellman's curse of dimensionality"e;, and so on.Neural Approximations for Optimal Control and Decision propounds a method of constraining the admissible control or decision functions to take on the structure of neural networks or other nonlinear approximators in which a certain number of parameters must be optimized: the "e;Extended Ritz Method"e; or ERIM. Using the ERIM, functional optimization problems are reduced to matters of nonlinear programming. By combining ideas drawn from functional optimization, optimal control, nonlinear approximation and data-based learning, computationally efficient approximation schemes are derived. Such schemes are expressible as combinations of simple computational units dependent on parameters like the weights in neural networks and are optimized with nonlinear programming algorithms.Features of the text include: an overview of classical computational methods: discrete dynamic programming, gradient techniques, the Ritz method etc.; a thorough illustration of recent theoretical insights into the approximate solutions of complex functional optimization problems; an organic comparison of classical and neural-network-based methods of approximate solution; a derivation of the theoretical properties of the ERIM, a novel methodology of functional optimization based on nonlinear approximators; bounds to the errors of approximate solutions; efficient solution algorithms for a range of problems: optimal control and decision in deterministic or stochastic environments with perfect or imperfect state measurements over a finite or infinite time horizon and with one decision maker or several; applications to major fields of current interest: routing in communications networks, freeway traffic control, water resource management, stochastic shortest paths, exploration of unknown environments, etc.; numerous examples - often dealing with real applications and developed in full numerical detail. The authors' diverse backgrounds in automatic control, systems theory and operations research lend the book a range of expertise and subject matter appealing to academics and graduate students in all those disciplines together with computer science and other areas of engineering.