Noisy Pairwise-Comparison Random Search for Smooth Nonconvex Optimization
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917230703280128 |
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| author | Bakkali, Taha El Bouftini, Rayane Zhang, Qiuyi Saadi, Omar |
| author_facet | Bakkali, Taha El Bouftini, Rayane Zhang, Qiuyi Saadi, Omar |
| contents | We consider minimizing high-dimensional smooth nonconvex objectives using only noisy pairwise comparisons. Unlike classical zeroth-order methods limited by the ambient dimension $d$, we propose Noisy-Comparison Random Search (NCRS), a direct-search method that exploits random line search to adapt to the intrinsic dimension $k \le d$. We establish novel non-convex convergence guarantees for approximate stationarity: under a uniform-margin oracle, NCRS attains $ε$-stationarity with complexity $\mathcal{O}(k/(p^{2}ε^{2}))$, explicitly replacing ambient dependence with the intrinsic dimension. Furthermore, we introduce a general tie-aware noise model where comparison quality degrades near ties; for this setting, we prove that a majority-vote variant of NCRS achieves $ε$-stationarity with complexity $\mathcal{O}(k^{2}/ε^{4})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21166 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Noisy Pairwise-Comparison Random Search for Smooth Nonconvex Optimization Bakkali, Taha El Bouftini, Rayane Zhang, Qiuyi Saadi, Omar Optimization and Control We consider minimizing high-dimensional smooth nonconvex objectives using only noisy pairwise comparisons. Unlike classical zeroth-order methods limited by the ambient dimension $d$, we propose Noisy-Comparison Random Search (NCRS), a direct-search method that exploits random line search to adapt to the intrinsic dimension $k \le d$. We establish novel non-convex convergence guarantees for approximate stationarity: under a uniform-margin oracle, NCRS attains $ε$-stationarity with complexity $\mathcal{O}(k/(p^{2}ε^{2}))$, explicitly replacing ambient dependence with the intrinsic dimension. Furthermore, we introduce a general tie-aware noise model where comparison quality degrades near ties; for this setting, we prove that a majority-vote variant of NCRS achieves $ε$-stationarity with complexity $\mathcal{O}(k^{2}/ε^{4})$. |
| title | Noisy Pairwise-Comparison Random Search for Smooth Nonconvex Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2601.21166 |