Zeroth-Order Constrained Optimization from a Control Perspective via Feedback Linearization
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912853889384448 |
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| author | Zhang, Runyu Zardini, Gioele Ozdaglar, Asuman Shamma, Jeff Li, Na |
| author_facet | Zhang, Runyu Zardini, Gioele Ozdaglar, Asuman Shamma, Jeff Li, Na |
| contents | Safe derivative-free optimization under unknown constraints is a fundamental challenge in modern learning and control. Existing zeroth-order (ZO) methods typically still assume access to a first-order oracle of the constraint functions or restrict attention to convex settings, leaving nonconvex optimization with black-box constraints largely unexplored. We propose the zeroth-order feedback-linearization (ZOFL) algorithm for ZO constrained optimization that enforces feasibility without access to the first-order oracle of the constraint functions and applies to both equality and inequality constraints. The proposed approach relies only on noisy, sample-based gradient estimates obtained via two-point estimators, yet provably guarantees constraint satisfaction under mild regularity conditions. It adopts a control-theoretic perspective on ZO constrained optimization and leverages feedback linearization, a nonlinear control technique, to enforce feasibility. Finite-time bounds on constraint violation and asymptotic global convergence guarantees are established for the ZOFL algorithm. A midpoint discretization variant is further developed to improve feasibility without sacrificing optimality. Empirical results demonstrate that ZOFL consistently outperforms standard ZO baselines, achieving competitive objective values while maintaining feasibility. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24056 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Zeroth-Order Constrained Optimization from a Control Perspective via Feedback Linearization Zhang, Runyu Zardini, Gioele Ozdaglar, Asuman Shamma, Jeff Li, Na Optimization and Control Systems and Control Safe derivative-free optimization under unknown constraints is a fundamental challenge in modern learning and control. Existing zeroth-order (ZO) methods typically still assume access to a first-order oracle of the constraint functions or restrict attention to convex settings, leaving nonconvex optimization with black-box constraints largely unexplored. We propose the zeroth-order feedback-linearization (ZOFL) algorithm for ZO constrained optimization that enforces feasibility without access to the first-order oracle of the constraint functions and applies to both equality and inequality constraints. The proposed approach relies only on noisy, sample-based gradient estimates obtained via two-point estimators, yet provably guarantees constraint satisfaction under mild regularity conditions. It adopts a control-theoretic perspective on ZO constrained optimization and leverages feedback linearization, a nonlinear control technique, to enforce feasibility. Finite-time bounds on constraint violation and asymptotic global convergence guarantees are established for the ZOFL algorithm. A midpoint discretization variant is further developed to improve feasibility without sacrificing optimality. Empirical results demonstrate that ZOFL consistently outperforms standard ZO baselines, achieving competitive objective values while maintaining feasibility. |
| title | Zeroth-Order Constrained Optimization from a Control Perspective via Feedback Linearization |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2509.24056 |