Escaping Saddle Points with Inequality Constraints via Noisy Sticky Projected Gradient Descent
Escaping Saddle Points with Inequality Constraints via Noisy Sticky Projected Gradient Descent
复制标题
通过嘈杂粘性投影梯度下降逃离具有不等式约束的鞍点
DOI：
--
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Chi Jin
中科院分区：
文献类型：
--
作者：
Dmitrii Avdiukhin;Chi Jin
本文首次分析了有限个不等式约束下光滑非凸优化一阶方法的收敛性。我们的算法对k个线性不等式约束使用~ O （1 ε 2 + k√ε）梯度评估，并收敛于(cid:15) -二阶平稳点的松弛定义（其中梯度和Hessian是相对于主动约束进行评估的）。
We give the first analysis of convergence of a first-order method in smooth non-convex optimization under a bounded number of inequality constraints. Our algorithm uses ˜ O ( 1 ε 2 + k √ ε ) gradient evaluations for k linear inequality constraints and converges to a relaxed definition of an (cid:15) -second- order stationary point (for which the gradient and the Hessian are evaluated with respect to active constraints).