Unified Compression Algorithm for Distributed Nonconvex Optimization: Generalized to 1-Bit, Saturation, and Bounded Noise
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914466925379584 |
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| author | Wang, Haonan Liwang, Minghui Hong, Yiguang Johansson, Karl H. Yi, Xinlei |
| author_facet | Wang, Haonan Liwang, Minghui Hong, Yiguang Johansson, Karl H. Yi, Xinlei |
| contents | In this paper, we propose a unified compression algorithm for distributed nonconvex opitmization with both the locally- and globally-bounded communication compressors, including 1-bit compressors, saturating quantizers, and the globally-bounded compressors with both relative and absolute compression errors, as well as additional arbitrary bounded noise. We provide a rigorous convergence analysis in nonconvex settings and establish linear convergence under the Polyak-Lojasiewicz (P-L) condition. Notably, we establish an $\mathcal{O}(1/\sqrt{T})$ convergence rate for the locally-bounded class in the distributed nonconvex setting, matching that achieved by the centralized algorithms with 1-bit compressors, where $T$ denotes the total number of iterations. Moreover, one initial uncompressed communication round further yields an order-wise improvement to $\mathcal{O}(1/T^{2/3})$. For the P-L setting and the globally-bounded class, we recover state-of-the-art convergence rates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10615 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Unified Compression Algorithm for Distributed Nonconvex Optimization: Generalized to 1-Bit, Saturation, and Bounded Noise Wang, Haonan Liwang, Minghui Hong, Yiguang Johansson, Karl H. Yi, Xinlei Optimization and Control In this paper, we propose a unified compression algorithm for distributed nonconvex opitmization with both the locally- and globally-bounded communication compressors, including 1-bit compressors, saturating quantizers, and the globally-bounded compressors with both relative and absolute compression errors, as well as additional arbitrary bounded noise. We provide a rigorous convergence analysis in nonconvex settings and establish linear convergence under the Polyak-Lojasiewicz (P-L) condition. Notably, we establish an $\mathcal{O}(1/\sqrt{T})$ convergence rate for the locally-bounded class in the distributed nonconvex setting, matching that achieved by the centralized algorithms with 1-bit compressors, where $T$ denotes the total number of iterations. Moreover, one initial uncompressed communication round further yields an order-wise improvement to $\mathcal{O}(1/T^{2/3})$. For the P-L setting and the globally-bounded class, we recover state-of-the-art convergence rates. |
| title | Unified Compression Algorithm for Distributed Nonconvex Optimization: Generalized to 1-Bit, Saturation, and Bounded Noise |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2604.10615 |