Convergence of Neural Network Policies for Risk--Reward Optimization
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918375969521664 |
|---|---|
| author | Chen, Chang Dang, Duy-Minh |
| author_facet | Chen, Chang Dang, Duy-Minh |
| contents | We develop a neural-network framework for multi-period risk--reward stochastic control problems with constrained two-step feedback policies that may be discontinuous in the state. We allow a broad class of objectives built on a finite-dimensional performance vector, including terminal and path-dependent statistics, with risk functionals admitting auxiliary-variable optimization representations (e.g.\ Conditional Value-at-Risk and buffered probability of exceedance) and optional moment dependence. Our approach parametrizes the two-step policy using two coupled feedforward networks with constraint-enforcing output layers, reducing the constrained control problem to unconstrained training over network parameters. Under mild regularity conditions, we prove that the empirical optimum of the NN-parametrized objective converges in probability to the true optimal value as network capacity and training sample size increase. The proof is modular, separating policy approximation, propagation through the controlled recursion, and preservation under the scalarized risk--reward objective. Numerical experiments confirm the predicted convergence-in-probability behavior, show close agreement between learned and reference control heat maps, and demonstrate out-of-sample robustness on a large independent scenario set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06563 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convergence of Neural Network Policies for Risk--Reward Optimization Chen, Chang Dang, Duy-Minh Computational Finance 93E20, 68T07, 90C15, 62G05 We develop a neural-network framework for multi-period risk--reward stochastic control problems with constrained two-step feedback policies that may be discontinuous in the state. We allow a broad class of objectives built on a finite-dimensional performance vector, including terminal and path-dependent statistics, with risk functionals admitting auxiliary-variable optimization representations (e.g.\ Conditional Value-at-Risk and buffered probability of exceedance) and optional moment dependence. Our approach parametrizes the two-step policy using two coupled feedforward networks with constraint-enforcing output layers, reducing the constrained control problem to unconstrained training over network parameters. Under mild regularity conditions, we prove that the empirical optimum of the NN-parametrized objective converges in probability to the true optimal value as network capacity and training sample size increase. The proof is modular, separating policy approximation, propagation through the controlled recursion, and preservation under the scalarized risk--reward objective. Numerical experiments confirm the predicted convergence-in-probability behavior, show close agreement between learned and reference control heat maps, and demonstrate out-of-sample robustness on a large independent scenario set. |
| title | Convergence of Neural Network Policies for Risk--Reward Optimization |
| topic | Computational Finance 93E20, 68T07, 90C15, 62G05 |
| url | https://arxiv.org/abs/2603.06563 |