scholarly journals On Concentration for (Regularized) Empirical Risk Minimization

Sankhya A ◽  
2017 ◽  
Vol 79 (2) ◽  
pp. 159-200 ◽  
Author(s):  
Sara van de Geer ◽  
Martin J. Wainwright
Keyword(s):  
Empirical Risk Minimization ◽  
Risk Minimization ◽  
Empirical Risk ◽  
Regularized Empirical Risk Minimization

scholarly journals Distributed Accelerated Proximal Coordinate Gradient Methods

2017 ◽  
Author(s):  
Yong Ren ◽  
Jun Zhu
Keyword(s):  
Optimization Problem ◽  
Gradient Methods ◽  
Empirical Risk Minimization ◽  
Risk Minimization ◽  
L1 Norm ◽  
Coordinate Descent Algorithm ◽  
Empirical Risk ◽  
Parallel Structures ◽  
Regularized Empirical Risk Minimization ◽  
Special Case

We develop a general accelerated proximal coordinate descent algorithm in distributed settings (Dis- APCG) for the optimization problem that minimizes the sum of two convex functions: the first part f is smooth with a gradient oracle, and the other one Ψ is separable with respect to blocks of coordinate and has a simple known structure (e.g., L1 norm). Our algorithm gets new accelerated convergence rate in the case that f is strongly con- vex by making use of modern parallel structures, and includes previous non-strongly case as a special case. We further present efficient implementations to avoid full-dimensional operations in each step, significantly reducing the computation cost. Experiments on the regularized empirical risk minimization problem demonstrate the effectiveness of our algorithm and match our theoretical findings.

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