A Stochastic Optimization Approach to Control-Affine Optimal Control Problems
Abstract
We consider control-affine optimal control problems on the torus, where the dynamics and cost functions are only accessed through samples. Starting from a weak formulation of such problems, we derive a dual, a primal, and a primal-dual formulation, compatible with stochastic optimization. We show convergence of stochastic first-order methods to the optimal value under generic conditions. In addition, we introduce a computable metric that upper-bounds the performance of suboptimal controllers produced during optimization, under additional regularity assumptions. Preliminary results show that the method can efficiently solve a simple control problem. Finally, we discuss conditions for the boundedness of the optimal occupation measure, a key assumption for the primal and primal-dual approaches.
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BibTeX
@misc{berthier2026stochastic,
title = {{A Stochastic Optimization Approach to Control-Affine Optimal Control Problems}},
author = {Eloïse Berthier and Ziad Kobeissi and Francis Bach},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29265},
eprint = {2609.29265},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05762216v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Stochastic Optimization Approach to Control-Affine Optimal Control Problems
AU - Eloïse Berthier
AU - Ziad Kobeissi
AU - Francis Bach
PY - 2026
DA - 2026/09/24
PB - HAL
DO - 10.48550/arxiv.2609.29265
UR - https://hal.science/hal-05762216v1
AB - We consider control-affine optimal control problems on the torus, where the dynamics and cost functions are only accessed through samples. Starting from a weak formulation of such problems, we derive a dual, a primal, and a primal-dual formulation, compatible with stochastic optimization. We show convergence of stochastic first-order methods to the optimal value under generic conditions. In addition, we introduce a computable metric that upper-bounds the performance of suboptimal controllers produced during optimization, under additional regularity assumptions. Preliminary results show that the method can efficiently solve a simple control problem. Finally, we discuss conditions for the boundedness of the optimal occupation measure, a key assumption for the primal and primal-dual approaches.
ER -