We develop simple differentially private optimization algorithms that move along directions of (expected) descent to find an approximate second-order solution for nonconvex ERM. We use line search, mini-batching, and a two-phase strategy to improve the speed and practicality of the algorithm. Numerical experiments demonstrate the effectiveness of these approaches.

翻译：我们开发了简单的差分隐私优化算法，该算法沿（期望）下降方向移动，为非凸经验风险最小化寻找近似二阶解。我们采用线性搜索、小批量处理和两阶段策略来提高算法的速度和实用性。数值实验证明了这些方法的有效性。