Report
A Gradient Descent-Ascent Method for Continuous-Time Risk-Averse Optimal Control
| العنوان: | A Gradient Descent-Ascent Method for Continuous-Time Risk-Averse Optimal Control |
|---|---|
| المؤلفون: | Velho, Gabriel, Auriol, Jean, Bonalli, Riccardo |
| المساهمون: | Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS) |
| المصدر: | https://hal.science/hal-04381732 ; 2024. |
| بيانات النشر: | HAL CCSD |
| سنة النشر: | 2024 |
| مصطلحات موضوعية: | Gradient descent-ascent Coherent risk measures Stochastic optimal control Non-linear control Risk-averse control, Gradient descent-ascent, Coherent risk measures, Stochastic optimal control, Non-linear control, Risk-averse control, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY] |
| الوصف: | In this paper, we consider continuous-time stochastic optimal control problems where the cost is evaluated through a coherent risk measure. We provide an explicit gradient descent-ascent algorithm which applies to problems subject to non-linear stochastic differential equations. More specifically, we leverage duality properties of coherent risk measures to relax the problem via a smooth min-max reformulation which induces artificial strong concavity in the max subproblem. We then formulate necessary conditions of optimality for this relaxed problem which we leverage to prove convergence of the gradient descent-ascent algorithm to candidate solutions of the original problem. Finally, we showcase the efficiency of our algorithm through numerical simulations involving trajectory tracking problems and highlight the benefit of favoring risk measures over classical expectation. |
| نوع الوثيقة: | report |
| اللغة: | English |
| Relation: | info:eu-repo/semantics/altIdentifier/arxiv/2306.12878; ARXIV: 2306.12878 |
| الاتاحة: | https://hal.science/hal-04381732 https://hal.science/hal-04381732v1/document https://hal.science/hal-04381732v1/file/2306.12878.pdf |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.D3476F2 |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |