一种基于ADMM的非光滑损失在线优化算法

交替方向乘子法（ADMM）在机器学习问题研究中已有一些高效的实际应用，但为了适应大规模数据的处理和求解非光滑损失凸优化问题，文中提出对原ADMM进行改进，得到了损失函数线性化的ADMM的在线优化算法。该在线算法相较原算法具有操作简单、计算高效等特点。通过详尽的理论分析，文中证明了新在线算法的收敛性，并得到其在一般凸条件下具有目前最优的Regret界以及随机收敛速度。最后在与当今流行在线算法的对比实验中验证了新在线算法的高效可行性。

A New Online Optimization Algorithm for Non-smooth Losses Based on ADMM

Alternating Direction Method of Multipliers （ADMM） already has some practical applications in machine learning problem. In order to adapt to the large-scale data processing and non -smooth loss convex optimization problem, the original batch ADMM has been improved ,and propose a new online ADMM with linearized loss function. This new algorithm has a simple operation and efficient computing. Through detailed theoretical analysis, prove the convergence of the new online algorithm and show it has the optimal Regret bound and convergence rate in general convex condition. Finally, compared with the state-of -art algorithms, verify it has efficiency and feasibility.