An Evolutionary Approach to Passive Learning in Optimal Control Problems

Abstract

This paper considers the optimal control problem of a small nonlinear econometric model under parameter uncertainty and passive learning (open-loop feedback). Traditionally, this type of problems has been approached by applying linear-quadratic optimization algorithms. However, the literature demonstrated that those methods are very sensitive to the choice of random seeds producing frequently very large objective function values (outliers). Furthermore, to apply those established methods the original nonlinear problem must be linearized first, which runs the risk of solving already a different problem. Following a recent study by Savin and Blueschke (2016) in explicitly addressing parameter uncertainty with a large Monte Carlo experiment of possible realizations of the uncertain parameter and minimizing it with the Differential Evolution algorithm, we extend this approach to the case of passive learning. Our conjecture is that the evolutionary approach can provide more robust results demonstrating greater benefit from learning, while at the same time does not require to modify the original nonlinear problem at hand. Our first results support this conjecture pointing to promising results in applying heuristic optimization methods to passive and active learning in optimal control research.