Stochastic Control of Linear and Nonlinear Econometric Models: Some Computational Aspects

Blueschke, Dmitri; Blueschke-Nikolaeva, V.; Neck, Reinhard

doi:10.1007/s10614-012-9351-x

Cited by 6 publications

(9 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, using DE one can extend the standard optimal control framework with an asymmetric or a non-quadratic objective function, and to include additional (inequality) constraints. In addition, we suggest that the new method is more robust to the outliers problem known in the optimal control experiments with learning strategies (see Tucci et al (2010) and Blueschke et al (2013a) for a detailed discussion of the topic). To demonstrate this, we use the ATOPT model and run a Monte Carlo experiment consisting of K draws of random disturbances (as explained in Algorithm 3) to compare DE_OLF, DE_OL, OLF and OL solutions.…”

Section: Results Of Comparison Between Optcon2 and Dementioning

confidence: 99%

An Evolutionary Approach to Passive Learning in Optimal Control Problems

2020

Self Cite

View full text Add to dashboard Cite

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).

show abstract

Section: Results Of Comparison Between Optcon2 and Dementioning

confidence: 99%

An Evolutionary Approach to Passive Learning in Optimal Control Problems

2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…For stochastic problems with adaptive control strategies, Tucci et al (2010) show that for some sets of parameters the problem is non-convex, which means that a local optimization method could be inappropriate. Some issues arising with nonlinear stochastic problems are shown in Blueschke et al (2013a), where the appearance of outliers in nonlinear optimal control problems is discussed. But extending the LQG framework to nonlinear problems raises additional concerns.…”

Section: Optconmentioning

confidence: 99%

“…To this end, we apply a similar procedure as performed by Blueschke et al (2013a) and multiply the covariance matrix Σ θθ (defined in Sect. 2) by a parameter ρ:…”

Section: Definitionmentioning

confidence: 99%

Lost in Translation: Explicitly Solving Nonlinear Stochastic Optimal Control Problems Using the Median Objective Value

Savin

Blueschke

2015

Comput Econ

View full text Add to dashboard Cite

Policy makers constantly face optimal control problems: what controls allow them to achieve certain targets in, e.g., GDP growth or inflation? Conventionally this is done by applying certain linear-quadratic optimization algorithms to dynamic econometric models. Several algorithms extend this baseline framework to nonlinear stochastic problems. However, those algorithms are limited in a variety of ways including, most importantly, their restriction to local best solutions only and the symmetry of objective function. The contribution of the current study is that we adopt differential evolution (DE) in the context of nonlinear stochastic optimal control problems, thus ensuring better convergence to a global optimum and explicitly considering parameter uncertainty by evaluating the expected objective function. The latter is done by minimizing the median over a set of multiple Monte Carlo draws of uncertain parameters and by separately evaluating the random parameter draws looking particularly at extreme cases. Comparing DE with more traditional methods, which make use of linear-quadratic optimization, in two economic models, we find that the solutions obtained for expected and ex-post functions differ consistently raising doubts about the optimality of ex-post solutions. We claim that this research is aimed to broaden B Ivan Savin the range of decision support information used by policy makers when choosing an optimal strategy under much more realistic conditions.

show abstract

“…For stochastic problems with adaptive control strategies Tucci et al (2010) show that the problem is non-convex, which means that a local optimization method could be not appropriate. Some problems of the nonlinear stochastic problems are shown in Blueschke et al (2013b), but there is even more to say concerning an extension to nonlinear problems. The OPTCON algorithm like all algorithms relying on LQG optimization technique solves the nonlinearity problem by a local linear approximation.…”

Section: Optconmentioning

confidence: 99%

“…To this end, we apply a similar procedure as it was performed by Blueschke et al (2013b) and multiply the covariance matrix Σ θθ (defined in Section 2) by a parameter ρ:…”

Section: In Other Words If One Function Is Monotonously Decreasing Omentioning

confidence: 99%

Solving Nonlinear Stochastic Optimal Control Problems Using Evolutionary Heuristic Optimization

Savin

Blueschke

2013

SSRN Journal

View full text Add to dashboard Cite

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Solving nonlinear stochastic optimal control problems using evolutionary heuristic optimization * I. Savin † ‡ and D. Blueschke § Abstract Policy makers constantly face optimal control problems: what controls allow to achieve certain targets in, e.g., GDP growth or inflation? Conventionally this is done by applying certain linear-quadratic optimization algorithms to dynamic econometric models. Several algorithms extend this baseline framework to nonlinear stochastic problems. However, those algorithms are limited in a variety of ways including, most importantly, restriction to local best solutions only and the symmetry of objective function. In Blueschke et al. (2013a) a new flexible optimization method based on Differential Evolution is suggested. It allows to lift these limitations and achieve better approximations of the policy targets, but is designed to deterministic problems only. This study extends the methodology by dealing with stochastic problems in two different ways: applying extreme event analysis and by minimizing the median objective value. Thus, this research is aimed to broaden the range of decision support information used by policy makers in choosing optimal strategy under much more realistic conditions. Terms of use: Documents in

show abstract

Stochastic Control of Linear and Nonlinear Econometric Models: Some Computational Aspects

Cited by 6 publications

References 7 publications

An Evolutionary Approach to Passive Learning in Optimal Control Problems

An Evolutionary Approach to Passive Learning in Optimal Control Problems

Lost in Translation: Explicitly Solving Nonlinear Stochastic Optimal Control Problems Using the Median Objective Value

Solving Nonlinear Stochastic Optimal Control Problems Using Evolutionary Heuristic Optimization

Contact Info

Product

Resources

About