Optimal control by policy improvements and constrained Gaussian process regressions

Donatien Hainaut () and Jean-Loup Dupret
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Donatien Hainaut: Université catholique de Louvain, LIDAM/ISBA, Belgium
Jean-Loup Dupret: ETH Zürich

No 2025012, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: This article proposes a new iterative algorithm combining policy improvements and Gaussian process regressions for solving stochastic control problems. At each iteration, we update an approximated value function and then improve the controls. We sample state variables in the inner domain and on the terminal boundary of the Hamilton-Jacobi-Bellman (HJB) equation. The approximated value function, the solution of this equation, is obtained by fitting a constrained regression function. The regression function matches the terminal utility on the boundary sample and satisfies the HJB equation on the inner sample. Assuming the regression function is a Gaussian process, we find a closed-form approximation of the value function and of the controls. In a numerical illustration, we test the efficiency of the method for solving the consumption-investment and linear-quadratic regulator problems.

Keywords: Optimal control; Gaussian process regression; Hamilton-Jacobi-Bellman equation; reinforcement learning; policy improvement (search for similar items in EconPapers)
Pages: 26
Date: 2025-05-12
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