Stochastic Non-Smooth Non-Convex Optimization with Decision-Dependent Distributions
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911658209705984 |
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| author | Liu, Chengchang Wan, Zongqi Ye, Haishan Lui, John C. S. |
| author_facet | Liu, Chengchang Wan, Zongqi Ye, Haishan Lui, John C. S. |
| contents | We study stochastic zeroth-order optimization with decision-dependent distributions, where the sampling law depends on the current decision and only noisy function values are available. For the non-smooth non-convex setting, we establish an explicit convergence guarantee for finding a $(δ,ε)$-Goldstein stationary point with stochastic zeroth-order oracle (SZO) complexity of $\mathcal{O}(d^2δ^{-3}ε^{-3})$. In addition, we show that the above complexity can be achieved with single SZO feedback per iteration. We further extend the analysis to smooth and Hessian-Lipschitz objectives, obtaining complexities $\mathcal{O}(d^2ε^{-6})$ and $\mathcal{O}(d^2ε^{-9/2})$, respectively. In the Hessian-Lipschitz case, this improves the best-known dependence on $ε$ for decision-dependent zeroth-order methods by a factor of $ε^{-1/2}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_06549 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic Non-Smooth Non-Convex Optimization with Decision-Dependent Distributions Liu, Chengchang Wan, Zongqi Ye, Haishan Lui, John C. S. Optimization and Control We study stochastic zeroth-order optimization with decision-dependent distributions, where the sampling law depends on the current decision and only noisy function values are available. For the non-smooth non-convex setting, we establish an explicit convergence guarantee for finding a $(δ,ε)$-Goldstein stationary point with stochastic zeroth-order oracle (SZO) complexity of $\mathcal{O}(d^2δ^{-3}ε^{-3})$. In addition, we show that the above complexity can be achieved with single SZO feedback per iteration. We further extend the analysis to smooth and Hessian-Lipschitz objectives, obtaining complexities $\mathcal{O}(d^2ε^{-6})$ and $\mathcal{O}(d^2ε^{-9/2})$, respectively. In the Hessian-Lipschitz case, this improves the best-known dependence on $ε$ for decision-dependent zeroth-order methods by a factor of $ε^{-1/2}$. |
| title | Stochastic Non-Smooth Non-Convex Optimization with Decision-Dependent Distributions |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2605.06549 |