Nonlinear Perturbation-based Non-Convex Optimization over Time-Varying Networks
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917741284294656 |
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| author | Doostmohammadian, Mohammadreza Gabidullina, Zulfiya R. Rabiee, Hamid R. |
| author_facet | Doostmohammadian, Mohammadreza Gabidullina, Zulfiya R. Rabiee, Hamid R. |
| contents | Decentralized optimization strategies are helpful for various applications, from networked estimation to distributed machine learning. This paper studies finite-sum minimization problems described over a network of nodes and proposes a computationally efficient algorithm that solves distributed convex problems and optimally finds the solution to locally non-convex objective functions. In contrast to batch gradient optimization in some literature, our algorithm is on a single-time scale with no extra inner consensus loop. It evaluates one gradient entry per node per time. Further, the algorithm addresses link-level nonlinearity representing, for example, logarithmic quantization of the exchanged data or clipping of the exchanged data bits. Leveraging perturbation-based theory and algebraic Laplacian network analysis proves optimal convergence and dynamics stability over time-varying and switching networks. The time-varying network setup might be due to packet drops or link failures. Despite the nonlinear nature of the dynamics, we prove exact convergence in the face of odd sign-preserving sector-bound nonlinear data transmission over the links. Illustrative numerical simulations further highlight our contributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02269 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlinear Perturbation-based Non-Convex Optimization over Time-Varying Networks Doostmohammadian, Mohammadreza Gabidullina, Zulfiya R. Rabiee, Hamid R. Systems and Control Distributed, Parallel, and Cluster Computing Signal Processing Optimization and Control Decentralized optimization strategies are helpful for various applications, from networked estimation to distributed machine learning. This paper studies finite-sum minimization problems described over a network of nodes and proposes a computationally efficient algorithm that solves distributed convex problems and optimally finds the solution to locally non-convex objective functions. In contrast to batch gradient optimization in some literature, our algorithm is on a single-time scale with no extra inner consensus loop. It evaluates one gradient entry per node per time. Further, the algorithm addresses link-level nonlinearity representing, for example, logarithmic quantization of the exchanged data or clipping of the exchanged data bits. Leveraging perturbation-based theory and algebraic Laplacian network analysis proves optimal convergence and dynamics stability over time-varying and switching networks. The time-varying network setup might be due to packet drops or link failures. Despite the nonlinear nature of the dynamics, we prove exact convergence in the face of odd sign-preserving sector-bound nonlinear data transmission over the links. Illustrative numerical simulations further highlight our contributions. |
| title | Nonlinear Perturbation-based Non-Convex Optimization over Time-Varying Networks |
| topic | Systems and Control Distributed, Parallel, and Cluster Computing Signal Processing Optimization and Control |
| url | https://arxiv.org/abs/2408.02269 |