论文标题
分布式梯度流：非平滑度，非洞穴性和弹跳点逃避
Distributed Gradient Flow: Nonsmoothness, Nonconvexity, and Saddle Point Evasion
论文作者
论文摘要
本文认为用于多代理非凸优化的分布式梯度流（DGF）。 DGF是分布式梯度下降的连续时间近似，通常比离散时间对应物更容易学习。该论文有两个主要贡献。首先，本文考虑了非滑动，非凸目标函数的优化。结果表明，在此设置中，DGF会收敛到关键点。然后，本文考虑了避免鞍点的问题。结果表明，如果假定代理的目标函数是平滑而非convex，则DGF只能从零量的初始条件集中收敛到鞍点。为了确定这一结果，本文证明了DGF的稳定歧管定理，这是独立利益的基本贡献。在同伴论文中，用于离散时间算法的类似结果。
The paper considers distributed gradient flow (DGF) for multi-agent nonconvex optimization. DGF is a continuous-time approximation of distributed gradient descent that is often easier to study than its discrete-time counterpart. The paper has two main contributions. First, the paper considers optimization of nonsmooth, nonconvex objective functions. It is shown that DGF converges to critical points in this setting. The paper then considers the problem of avoiding saddle points. It is shown that if agents' objective functions are assumed to be smooth and nonconvex, then DGF can only converge to a saddle point from a zero-measure set of initial conditions. To establish this result, the paper proves a stable manifold theorem for DGF, which is a fundamental contribution of independent interest. In a companion paper, analogous results are derived for discrete-time algorithms.
