NIPS 2018
Sun Dec 2nd through Sat the 8th, 2018 at Palais des Congrès de Montréal
Paper ID: 2380 On the Local Minima of the Empirical Risk

### Reviewer 2

Population risk is ultimately of interest in machine learning and statistics, while a direct optimization acting at the population risk is impossible due to some unknown measurements, or it is unreasonable due to the purpose of privacy preservation. This paper is to find an approximate Local minima of the underling function $F$ by implementing a simple zero-order SGD for an approximate function of $F$. Moreover, the authors proved that the proposed algorithm is optimal under some framework. Finally, they provided a popular example to show their theoretical results clearly. In summary, I believe that the current paper is well written and has significant contribution in the literature of nonvex optimization, and particularly established some deep theoretical concussions for their proposed algorithm.

### Reviewer 3

This paper studies the problem of minimizing the population risk by the proposed ZPSGD algorithm. The main contribution of this work is the new algorithm that can find an \epsilon approximate local minima of this nonconvex optimization problem. The paper is well-written but lacks the numerical results which can show the superiority of the proposed methods compared with the existing works.