Value Function Iteration Using Tensor Train Decomposition

Richard Dennis

CAMA Working Papers from Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University

Abstract: This paper presents a novel approach to solving dynamic programming problems using value function iteration based on the tensor train decomposition. The tensor train decomposition approximates high-dimensional functions by expressing them as a series of interconnected cores, producing an approximation that separates by variables. This approach is well-suited for approximating and integrating high-dimensional functions, such as a value function. We apply the method to a range of models and compare its performance against established sparse-grid techniques involving Smolyak and hyperbolic cross polynomials and neural networks. For models with as few as three state variables, the tensor train method is shown to be faster and/or more accurate than the leading sparse-grid alternatives. This paper shows how tensor train methods can be used to solve dynamic optimization problems in Economics, offering a powerful approach to solve high-dimensional macroeconomic models.

Keywords: value function iteration; tensor train decomposition; curse of dimensionality (search for similar items in EconPapers)
JEL-codes: C61 C63 (search for similar items in EconPapers)
Pages: 47 pages
Date: 2026-02, Revised 2026-09
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https://crawford.anu.edu.au/sites/default/files/2026-09/12_2026_Dennis_2.pdf Revised Version (application/pdf)
https://crawford.anu.edu.au/sites/default/files/2026-09/12a_2026_Dennis.pdf Original Version (application/pdf)

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Persistent link: https://EconPapers.repec.org/RePEc:een:camaaa:2026-12

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