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An Evolutionary Approach to Passive Learning in Optimal Control Problems

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Listed:
  • D. Blueschke

    () (University of Klagenfurt)

  • I. Savin

    () (Universitat Autónoma de Barcelona
    Ural Federal University)

  • V. Blueschke-Nikolaeva

    (University of Klagenfurt)

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.

Suggested Citation

  • D. Blueschke & I. Savin & V. Blueschke-Nikolaeva, 2020. "An Evolutionary Approach to Passive Learning in Optimal Control Problems," Computational Economics, Springer;Society for Computational Economics, vol. 56(3), pages 659-673, October.
  • Handle: RePEc:kap:compec:v:56:y:2020:i:3:d:10.1007_s10614-019-09961-4
    DOI: 10.1007/s10614-019-09961-4
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    References listed on IDEAS

    as
    1. Tucci, Marco P. & Kendrick, David A. & Amman, Hans M., 2010. "The parameter set in an adaptive control Monte Carlo experiment: Some considerations," Journal of Economic Dynamics and Control, Elsevier, vol. 34(9), pages 1531-1549, September.
    2. Amman, Hans M. & Kendrick, David A., 2003. "Mitigation of the Lucas critique with stochastic control methods," Journal of Economic Dynamics and Control, Elsevier, vol. 27(11), pages 2035-2057.
    3. Manfred Gilli & Enrico Schumann, 2009. "Optimal enough?," Working Papers 010, COMISEF.
    4. Blueschke-Nikolaeva, V. & Blueschke, D. & Neck, R., 2012. "Optimal control of nonlinear dynamic econometric models: An algorithm and an application," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3230-3240.
    5. Hans M. Amman & Marco Paolo Tucci, 2018. "How active is active learning: value function method vs an approximation method," Department of Economics University of Siena 788, Department of Economics, University of Siena.
    6. Ilzetzki, Ethan & Mendoza, Enrique G. & Végh, Carlos A., 2013. "How big (small?) are fiscal multipliers?," Journal of Monetary Economics, Elsevier, vol. 60(2), pages 239-254.
    7. Beck, Gunter W. & Wieland, Volker, 2002. "Learning and control in a changing economic environment," Journal of Economic Dynamics and Control, Elsevier, vol. 26(9-10), pages 1359-1377, August.
    8. Dimitri Blueschke & Viktoria Blüschke-Nikolaeva & Ivan Savin, 2015. "Slow and steady wins the race: approximating Nash equilibria in nonlinear quadratic tracking games," Jena Economic Research Papers 2015-011, Friedrich-Schiller-University Jena.
    9. David Kendrick & Hans Amman, 2006. "A Classification System for Economic Stochastic Control Models," Computational Economics, Springer;Society for Computational Economics, vol. 27(4), pages 453-481, June.
    10. Savin Ivan, 2013. "A Comparative Study of the Lasso-type and Heuristic Model Selection Methods," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 233(4), pages 526-549, August.
    11. Ivan Savin & Dmitri Blueschke, 2016. "Lost in Translation: Explicitly Solving Nonlinear Stochastic Optimal Control Problems Using the Median Objective Value," Computational Economics, Springer;Society for Computational Economics, vol. 48(2), pages 317-338, August.
    12. Blueschke, D. & Blueschke-Nikolaeva, V. & Savin, I., 2013. "New insights into optimal control of nonlinear dynamic econometric models: Application of a heuristic approach," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 821-837.
    13. Emi Nakamura & J?n Steinsson, 2014. "Fiscal Stimulus in a Monetary Union: Evidence from US Regions," American Economic Review, American Economic Association, vol. 104(3), pages 753-792, March.
    14. D. Blueschke & I. Savin, 2017. "No such thing as a perfect hammer: comparing different objective function specifications for optimal control," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(2), pages 377-392, June.
    15. D. Blueschke & V. Blueschke-Nikolaeva & R. Neck, 2013. "Stochastic Control of Linear and Nonlinear Econometric Models: Some Computational Aspects," Computational Economics, Springer;Society for Computational Economics, vol. 42(1), pages 107-118, June.
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    Cited by:

    1. V. Blueschke-Nikolaeva & D. Blueschke & R. Neck, 2020. "OPTCON3: An Active Learning Control Algorithm for Nonlinear Quadratic Stochastic Problems," Computational Economics, Springer;Society for Computational Economics, vol. 56(1), pages 145-162, June.

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