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arXiv · 2609.29265

A Stochastic Optimization Approach to Control-Affine Optimal Control Problems

Eloïse Berthier·Ziad Kobeissi·Francis Bach
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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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Eloïse Berthier, Ziad Kobeissi, Francis Bach. 2026-09-24. A Stochastic Optimization Approach to Control-Affine Optimal Control Problems. https://arxiv.org/abs/2609.29265

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