Using Deep Learning Neural Networks to Solve Optimization Problems in Economy
Main Article Content
Abstract
Abstract: In this work, we have used multilayer neural networks to solve high-dimensional dynamic programming problems. We propose a deep learning algorithm to efficiently compute the overall solution for this class of problems. Importantly, our method does not rely on integral approximation but instead on derivative approximation. We evaluate the effectiveness of the proposed method through the standard neoclassical growth model.
Optimization, HJB equation, machine learning, neural network.
Keywords:
Optimization, HJB equation, machine learning, Optimization, HJB equation, machine learning, neural network.
References
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[3] J. Brumm, S. Scheidegger, Using Adaptive Sparse Grids to Solve HighDimensional Dynamic Models, Econometrica, Vol. 85, 2017, pp. 1575-1612.
[4] W. D. Haan, A. Marcet, Solving the Stochastic Growth Model by Parameterized Expectations, Journal of Business and Economic Statistics, Vol. 8, pp. 31-34.
[5] L. Maliar, S. Maliar, Parameterized Expectations Algorithm: How to Solve for Labor Easily, Computational Economics, Vol. 25, 2005, pp. 269-274.
[6] K. L. Judd, L. Maliar, S. Maliar, Numerically Stable and Accurate Stochastic Simulation Approaches for Solving Dynamic Models, Quant Econom, Vol. 2, 2011, pp. 173-210.
[7] L. Maliar, S. Maliar, Merging Simulation and Projection Approaches to Solve High-dimensional Problems with an Application to A New Keynesian Model, Quant Econom, Vol. 6, 2015, pp. 1-47.
[8] A. Jirniy, V. Lepetyuk, A Reinforcement Learning Approach to Solving Incomplete Market Models with Aggregate Uncertainty, SSRN: https://papers. ssrn.com/sol3/papers.cfm?abstract_id=1832745, 2011 (accessed on: April 1st, 2024).
[9] P. Krusell, A. Smith, Income and Wealth Heterogeneity in the Macroeconomy, Journal of Political Economy, Vol. 106, 1998, pp. 868-896.
[10] J. Duffy, P. McNelis, Approximating and Simulating the Real Business Cycle Model: Parameterized Expectations, Neural Networks, and the Geneticalgorithm, Journal of Economic Dynamics and Control, Vol. 25, No. 9, 2001, pp. 1273-1303.
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[14] A. Villa, V. Valaitis, Machine Learning Projection Methods for Macro-Finance Models. SSRN: https://papers.ssrn.com/sol3/papers.cfm?abstract_id= 3209934, 2019 (accessed on: April 1st, 2024).
[15] M. Azinovic, J. Luca, S. Scheidegger, Deep Equilibrium Nets, SSRN: https://ssrn.com/abstract=3393482, 2020 (accessed on: April 1st, 2024).