{"ID":6536412,"CreatedAt":"2026-07-14T01:21:01.169441415Z","UpdatedAt":"2026-07-14T10:34:48.424166754Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.10254","arxiv_id":"2607.10254","title":"Neural feedback approximation for stochastic control with degenerate diffusions: error estimates and numerical analysis","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.","short_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 induc...","url_abs":"https://arxiv.org/abs/2607.10254","url_pdf":"https://arxiv.org/pdf/2607.10254v1","authors":"[\"Olivier Bokanowski\",\"Jean-François Chassagneux\",\"Marco Scaratti\",\"Xavier Warin\"]","published":"2026-07-11T10:45:22Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.NA\"]","methods":"[\"Diffusion Model\",\"Large Language Model\"]","has_code":false}