SCOPE: Scalable Composite Optimization for Learning on Spark

Many machine learning models, such as logistic regression~(LR) and support vector machine~(SVM), can be formulated as composite optimization problems. Recently, many distributed stochastic optimization~(DSO) methods have been proposed to solve the large-scale composite optimization problems, which have shown better performance than traditional batch methods. However, most of these DSO methods are not scalable enough. In this paper, we propose a novel DSO method, called \underline{s}calable \underline{c}omposite \underline{op}timization for l\underline{e}arning~({SCOPE}), and implement it on the fault-tolerant distributed platform \mbox{Spark}. SCOPE is both computation-efficient and communication-efficient. Theoretical analysis shows that SCOPE is convergent with linear convergence rate when the objective function is convex. Furthermore, empirical results on real datasets show that SCOPE can outperform other state-of-the-art distributed learning methods on Spark, including both batch learning methods and DSO methods

Σ\Sigma Resonances from K−N→πΛK^- N\rightarrow \pi\Lambda reactions with the center of mass energy from 1550 to 1676 MeV

For the study of the $\Sigma$ resonances, we analyze the differential cross sections and $\Lambda$ polarizations for the reactions $K^-n\to\pi^-\Lambda$ and $K^-p\to\pi^0\Lambda$ with an effective Lagrangian approach. Data of an early experiment and the recent Crystal Ball experiment at BNL are included in the analysis with the c.m. energy from 1550 to 1676 MeV. Our results clearly support the existence of a $\Sigma$ resonance with $J^P={1\over 2}^+$, mass near 1633 MeV, and width about 120 MeV, which confirms the 3-star $\Sigma(1660) 1/2^+$ in PDG. Meanwhile, our results do not support the existence of the 2-star $\Sigma(1620){1\over 2}^-$ in PDG. The analysis results for the parameters of the relevant $\Sigma$ resonances and couplings are presented.Comment: version accepted by Phys. Rev.