发表机构
School of Automation, Southeast University; China Industrial Control Systems Cyber Emergency Response Team（东南大学自动化学院; 中国工业控制系统信息安全应急响应中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对有向不平衡图上信息共享噪声导致梯度跟踪噪声累积和左特征向量缩放失真的问题，提出仅用行随机权重的R-Xi-row算法，通过辅助变量增量更新和衰减增益，实现强凸光滑目标下几乎必然收敛并达到近O(k^{-1/3})期望速率。
AI 中文摘要
在存在信息共享噪声的情况下，针对有向且不平衡图的行随机分布式优化不仅会遭受梯度跟踪中噪声累积的影响，还会因用于不平衡补偿的左特征向量梯度缩放被扭曲而受损。为解决这些问题，本文提出了一种仅使用行随机权重的抗噪分布式优化算法，称为Robust Xi-row（R-Xi-row）。优化更新由辅助累积变量的增量驱动，以排除历史跟踪噪声，同时使用两个衰减增益和一个归一化缩放增益来抑制噪声特征向量估计的影响，并几乎必然地渐近恢复所需的梯度缩放。在强凸且光滑的目标函数和适当的衰减增益下，我们证明了几乎必然收敛到最优解。对于多项式衰减增益，我们进一步建立了接近$\mathcal{O}(k^{-1/3})$的期望收敛速率。数值实验验证了理论结果。
英文摘要
In the presence of information-sharing noise, row-stochastic distributed optimization over directed and unbalanced graphs can suffer not only from noise accumulation in gradient tracking, but also from distortion of the left eigenvector-based gradient scaling used for imbalance compensation. To address these issues, this paper proposes a noise-robust distributed optimization algorithm using only row-stochastic weights, termed Robust Xi-row (R-Xi-row). The optimization update is driven by the increment of an auxiliary cumulative variable to exclude historical tracking noise, while two decaying gains and a normalized scaling gain are used to suppress the effect of noisy eigenvector estimation and asymptotically recover the required gradient scaling almost surely. Under strongly convex and smooth objectives and appropriate decaying gains, we prove almost sure convergence to the optimal solution. For polynomially decaying gains, we further establish a near-$\mathcal{O}(k^{-1/3})$ expected convergence rate. Numerical experiments validate the theoretical results.
