Optimal control by policy iterations and constrained Gaussian process regressions
(2026) European Journal of Operational Research — Vol. 330, n° 2, p. 525-539 (2026)
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- Authors
Dupret, Jean-Loup 
- Abstract
- This article introduces a novel iterative algorithm that combines policy iterations with Gaussian process regressions to solve stochastic control problems. At each iteration, an approximate value function is updated, followed by an improvement of the control strategy. State variables are sampled both within the interior domain and on the terminal boundary of the Hamilton-Jacobi-Bellman (HJB) equation. The approximate value function, interpreted as the solution to the HJB equation, is obtained by fitting a constrained regression model. This regression function aligns with the terminal utility on the boundary sample and satisfies the HJB equation on the interior sample. Assuming the regression function follows a Gaussian process, we derive closed-form approximations for both the value function and its derivatives. A numerical illustration demonstrates the efficiency of the proposed method in solving the consumption-investment problem, the linear-quadratic regulator, and a constrained consumption-investment problem with stochastic volatility. As benchmarks, we compare our results with those obtained using backward partial differential equation (PDE) methods and Physics-Informed Neural Networks (PINNs).
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Citations
Hainaut, D., & Dupret, J.-L. (2026). Optimal control by policy iterations and constrained Gaussian process regressions. European Journal of Operational Research, 330(2), 525-539. https://doi.org/10.1016/j.ejor.2025.12.001 (Original work published 2026)