A Comprehensive Linear Speedup Analysis for Asynchronous Stochastic   Parallel Optimization from Zeroth-Order to First-Order
  Asynchronous parallel optimization received substantial successes and extensive attention recently. One of core theoretical questions is how much speedup (or benefit) the asynchronous parallelization can bring us. This paper provides a comprehensive and generic analysis to study the speedup property for a broad range of asynchronous parallel stochastic algorithms from the zeroth order to the first order methods. Our result recovers or improves existing analysis on special cases, provides more insights for understanding the asynchronous parallel behaviors, and suggests a novel asynchronous parallel zeroth order method for the first time. Our experiments provide novel applications including model blending problems using the proposed asynchronous parallel zeroth order method. 
Xiangru Lian, Huan Zhang, Cho-Jui Hsieh, Yijun Huang, Ji Liu
math.OC