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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | https://arxiv.org/abs/2605.25306 |
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| _version_ | 1866910263212507136 |
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| author | Zhang, Shengjun Liu, Tingyi Zhang, Heng Xie, Dong |
| author_facet | Zhang, Shengjun Liu, Tingyi Zhang, Heng Xie, Dong |
| contents | This letter studies distributed stochastic optimization over a peer-to-peer network when agents can query only zeroth-order function values. We propose ZOOM-PB, a coordinate-sampling distributed zeroth-order method equipped with a fractional-power powerball map. Unlike existing distributed zeroth-order methods that mainly refine gradient estimation or introduce primal--dual tracking, the proposed mechanism acts as a nonlinear feedback gain on the estimated gradient: it amplifies weak signals in flat regions and attenuates large stochastic estimates without adding transmitted states. Under standard smoothness, oracle-variance, and network-connectivity assumptions, ZOOM-PB achieves the leading nonconvex stationarity rate $\mathcal{O}(\sqrt{p/(nT)})$, where $p$ is the decision dimension, $n$ is the number of agents, and $T$ is the iteration horizon. Under the Polyak--Łojasiewicz condition, it further attains the leading objective residual rate $\mathcal{O}(p/(nT))$. Thus the method preserves the known distributed ZO order while changing the finite-time behavior through a local nonlinear control gain. Simulations on black-box learning and sensor-driven UAV source seeking show faster empirical convergence in weak-signal regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25306 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonlinear-Gain Distributed Zeroth-Order Optimization for Networked Black-Box Control Zhang, Shengjun Liu, Tingyi Zhang, Heng Xie, Dong Systems and Control This letter studies distributed stochastic optimization over a peer-to-peer network when agents can query only zeroth-order function values. We propose ZOOM-PB, a coordinate-sampling distributed zeroth-order method equipped with a fractional-power powerball map. Unlike existing distributed zeroth-order methods that mainly refine gradient estimation or introduce primal--dual tracking, the proposed mechanism acts as a nonlinear feedback gain on the estimated gradient: it amplifies weak signals in flat regions and attenuates large stochastic estimates without adding transmitted states. Under standard smoothness, oracle-variance, and network-connectivity assumptions, ZOOM-PB achieves the leading nonconvex stationarity rate $\mathcal{O}(\sqrt{p/(nT)})$, where $p$ is the decision dimension, $n$ is the number of agents, and $T$ is the iteration horizon. Under the Polyak--Łojasiewicz condition, it further attains the leading objective residual rate $\mathcal{O}(p/(nT))$. Thus the method preserves the known distributed ZO order while changing the finite-time behavior through a local nonlinear control gain. Simulations on black-box learning and sensor-driven UAV source seeking show faster empirical convergence in weak-signal regimes. |
| title | Nonlinear-Gain Distributed Zeroth-Order Optimization for Networked Black-Box Control |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2605.25306 |