Neural Regression and Randomized Optimization for Impulse Control
Abstract
We develop a regression-based Monte Carlo framework for stochastic impulse control problems with controls taking values in a compact set. The method combines dynamic programming over discrete intervention times, neural networks to estimate continuation values, and a randomized search to select interventions. We first establish a time-discretization result for δ-separated strategies, proving an approximation error of order O(h^1/2 ), with h the mesh of the discretization. On the discrete grid, we derive a dynamic programming representation of the solution in terms of intervention regions and iteratively defined stopping rules, together with a verification lemma characterizing optimal strategies. Building on this representation, we introduce a backward numerical algorithm in the spirit of regression Monte Carlo methods, and extend it to controllers constrained to a finite intervention budget. For piecewise affine intervention objectives, we derive a direct geometric bound on the error introduced by the randomized selection step. Numerical experiments on classical dividend-distribution and harvesting problems are reported in dimensions up to six. In the reported out-of-sample policy comparisons in dimensions one and six, the learned policies outperform the grid-restricted stationary band benchmark under the corresponding finite-horizon criteria.
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BibTeX
@misc{abbasturki2026neural,
title = {{Neural Regression and Randomized Optimization for Impulse Control}},
author = {Lokman Abbas-Turki and Aurélien Grenard and Idris Kharroubi and Qinghua Li and Antonio Ocello},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05773012v1},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Neural Regression and Randomized Optimization for Impulse Control
AU - Lokman Abbas-Turki
AU - Aurélien Grenard
AU - Idris Kharroubi
AU - Qinghua Li
AU - Antonio Ocello
PY - 2026
DA - 2026/10/01
PB - HAL
UR - https://hal.science/hal-05773012v1
AB - We develop a regression-based Monte Carlo framework for stochastic impulse control problems with controls taking values in a compact set. The method combines dynamic programming over discrete intervention times, neural networks to estimate continuation values, and a randomized search to select interventions. We first establish a time-discretization result for δ-separated strategies, proving an approximation error of order O(h^1/2 ), with h the mesh of the discretization. On the discrete grid, we derive a dynamic programming representation of the solution in terms of intervention regions and iteratively defined stopping rules, together with a verification lemma characterizing optimal strategies. Building on this representation, we introduce a backward numerical algorithm in the spirit of regression Monte Carlo methods, and extend it to controllers constrained to a finite intervention budget. For piecewise affine intervention objectives, we derive a direct geometric bound on the error introduced by the randomized selection step. Numerical experiments on classical dividend-distribution and harvesting problems are reported in dimensions up to six. In the reported out-of-sample policy comparisons in dimensions one and six, the learned policies outperform the grid-restricted stationary band benchmark under the corresponding finite-horizon criteria.
ER -