An Evolutionary Approach to Passive Learning in Optimal Control Problems
- PDF / 513,837 Bytes
- 15 Pages / 439.37 x 666.142 pts Page_size
- 53 Downloads / 233 Views
An Evolutionary Approach to Passive Learning in Optimal Control Problems D. Blueschke1 · I. Savin2,3 · V. Blueschke-Nikolaeva1 Accepted: 16 November 2019 © The Author(s) 2019
Abstract We consider 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 frequently producing 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 Savin and Blueschke (Comput Econ 48(2):317–338, 2016) in explicitly addressing parameter uncertainty with a large Monte Carlo experiment of possible parameter realizations and optimizing it with the Differential Evolution algorithm, we extend this approach to the case of passive learning. Our approach provides more robust results demonstrating greater benefit from learning, while at the same time does not require to modify the original nonlinear problem at hand. This result opens new avenues for application of heuristic optimization methods to learning strategies in optimal control research.
I.S. acknowledges support from an ERC Advanced Grant under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement Nr. 741087) and the grant from the President of the Russian Federation for the support of young scientists number MD-3196.2019.6. V.B.-N. acknowledges support from the Austrian Science Fund (FWF) and Carinthian Economic Development Fund (KWF) (T 1012-GBL Hertha-Firnberg-Program).
B
D. Blueschke [email protected] I. Savin [email protected]
1
University of Klagenfurt, Klagenfurt, Austria
2
Institute of Environmental Science and Technology, Universitat Autónoma de Barcelona, Cerdanyola del Vallès, Spain
3
Graduate School of Economics and Management, Ural Federal University, Yekaterinburg, Russian Federation
123
D. Blueschke et al.
Keywords Optimal control · Stochastic problems · Differential Evolution · Passive learning
1 Introduction Mathematical models are pervasive in economics. They are often given in a form of a dynamic system of equations describing how economy evolves over time. Since it is widely accepted that the nonlinear framework allows to derive more precise picture of reality compared to the linear one, we consider a system of nonlinear equations describing an economy. Having such a mathematical system, one is tempted to use it in order to optimize the state of the world or rather to guide it into a desired direction. This is a very simplified description of the optimal control framework. One important topic in this research field is the inclusion of learning strategies. We follow this line of research and introduce in this study a new way for including a passive learning s
Data Loading...
