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arXiv · 2607.10254

Neural feedback approximation for stochastic control with degenerate diffusions: error estimates and numerical analysis

Olivier Bokanowski·Jean-François Chassagneux·Marco Scaratti·Xavier Warin
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Abstract

We study finite-horizon stochastic optimal control problems and approximate the resulting time-discrete formulation by a direct policy-learning problem over neural-network feedback maps. We prove a quantitative convergence estimate, in an averaged sense, for the error between the time-discrete value and the value induced by an approximately optimized neural policy. The bound separates the approximation of near-optimal feedback policies, the localization of stochastic trajectories on compact sets, and the optimization tolerance in training. The analysis does not require transition-density assumptions and covers possibly degenerate diffusions and deterministic controlled dynamics in a unified framework. Numerical experiments are provided for a degenerate stochastic radial target problem, a Hamilton--Jacobi--Bellman benchmark, and a gas storage problem, illustrating the approach and separating the main error sources: time discretization, restriction to piecewise-constant policies, neural-network approximation, and Monte Carlo evaluation.

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Olivier Bokanowski, Jean-François Chassagneux, Marco Scaratti, Xavier Warin. 2026-07-11. Neural feedback approximation for stochastic control with degenerate diffusions: error estimates and numerical analysis. https://arxiv.org/abs/2607.10254

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