Nonlinear Perturbation-based Non-Convex Optimization over Time-Varying Networks
<|reference_start|>Nonlinear Perturbation-based Non-Convex Optimization over Time-Varying Networks: 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.<|reference_end|>
@article{doostmohammadian2024nonlinear,
    title={Nonlinear Perturbation-based Non-Convex Optimization over Time-Varying
  Networks},
    author={Mohammadreza Doostmohammadian, Zulfiya R. Gabidullina, Hamid R. Rabiee},
    journal={arXiv preprint arXiv:2408.02269},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.02269},
    primaryClass={eess.SY cs.DC cs.SY eess.SP math.OC}
}