Safe Zeroth-Order Optimization Using Quadratic Local Approximations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909179379187712 |
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| author | Guo, Baiwei Jiang, Yuning Ferrari-Trecate, Giancarlo Kamgarpour, Maryam |
| author_facet | Guo, Baiwei Jiang, Yuning Ferrari-Trecate, Giancarlo Kamgarpour, Maryam |
| contents | This paper addresses black-box smooth optimization problems, where the objective and constraint functions are not explicitly known but can be queried. The main goal of this work is to generate a sequence of feasible points converging towards a KKT primal-dual pair. Assuming to have prior knowledge on the smoothness of the unknown objective and constraints, we propose a novel zeroth-order method that iteratively computes quadratic approximations of the constraint functions, constructs local feasible sets and optimizes over them. Under some mild assumptions, we prove that this method returns an $η$-KKT pair (a property reflecting how close a primal-dual pair is to the exact KKT condition) within $O({1}/{η^{2}})$ iterations. Moreover, we numerically show that our method can achieve faster convergence compared with some state-of-the-art zeroth-order approaches. The effectiveness of the proposed approach is also illustrated by applying it to nonconvex optimization problems in optimal control and power system operation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_16659 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Safe Zeroth-Order Optimization Using Quadratic Local Approximations Guo, Baiwei Jiang, Yuning Ferrari-Trecate, Giancarlo Kamgarpour, Maryam Optimization and Control Systems and Control This paper addresses black-box smooth optimization problems, where the objective and constraint functions are not explicitly known but can be queried. The main goal of this work is to generate a sequence of feasible points converging towards a KKT primal-dual pair. Assuming to have prior knowledge on the smoothness of the unknown objective and constraints, we propose a novel zeroth-order method that iteratively computes quadratic approximations of the constraint functions, constructs local feasible sets and optimizes over them. Under some mild assumptions, we prove that this method returns an $η$-KKT pair (a property reflecting how close a primal-dual pair is to the exact KKT condition) within $O({1}/{η^{2}})$ iterations. Moreover, we numerically show that our method can achieve faster convergence compared with some state-of-the-art zeroth-order approaches. The effectiveness of the proposed approach is also illustrated by applying it to nonconvex optimization problems in optimal control and power system operation. |
| title | Safe Zeroth-Order Optimization Using Quadratic Local Approximations |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2303.16659 |