Can a One-Point Feedback Zeroth-order Algorithm Achieve Linear Dimension Dependent Sample Complexity?
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918126405287936 |
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| author | Ye, Haishan Chang, Xiangyu |
| author_facet | Ye, Haishan Chang, Xiangyu |
| contents | We revisit the one-point feedback zeroth-order (ZO) optimization problem, a classical setting in derivative-free optimization where only a single noisy function evaluation is available per query. Compared to their two-point counterparts, existing one-point feedback ZO algorithms typically suffer from poor dimension dependence in their sample complexities -- often quadratic or worse -- even for convex problems. This gap has led to the open question of whether one-point feedback ZO algorithms can match the optimal \emph{linear} dimension dependence achieved by two-point methods. In this work, we answer this question \emph{affirmatively}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12228 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Can a One-Point Feedback Zeroth-order Algorithm Achieve Linear Dimension Dependent Sample Complexity? Ye, Haishan Chang, Xiangyu Optimization and Control We revisit the one-point feedback zeroth-order (ZO) optimization problem, a classical setting in derivative-free optimization where only a single noisy function evaluation is available per query. Compared to their two-point counterparts, existing one-point feedback ZO algorithms typically suffer from poor dimension dependence in their sample complexities -- often quadratic or worse -- even for convex problems. This gap has led to the open question of whether one-point feedback ZO algorithms can match the optimal \emph{linear} dimension dependence achieved by two-point methods. In this work, we answer this question \emph{affirmatively}. |
| title | Can a One-Point Feedback Zeroth-order Algorithm Achieve Linear Dimension Dependent Sample Complexity? |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2508.12228 |