基于交替方向乘子法的非光滑损失坐标优化算法.docx

基于交替方向乘子法的非光滑损失坐标优化算法文章编号：10019081（2013）07191205doi：10.11772/j.issn.10019081.2013.07.1912摘要：交替方向乘子法（ADMM）在机器学习问题中已有一些实际应用。针对大规模数据的处理和非光滑损失凸优化问题将镜面下降方法引入原ADMM批处理算法得到了一种新的改进算法并在此基础上提出了一种求解非光滑损失凸优化问题的坐标优化算法。该算法具有操作简单、计算高效的特点。通过详尽的理论分析证明了新算法的收敛性在一般凸条件下其具有目前最优的收敛速度。最后与相关算法进行了对比实验结果表明该算法在保证解稀疏性的同时拥有更快的收敛速度。关键词：机器学习；交替方向乘子法；坐标优化；大规模；非光滑损失中图分类号：TP301文献标志码：A英文标题Newcoordinateoptimizationmethodfornonsmoothlossesbasedonalternatingdirectionmethodofmultipliers英文作者名GAOQiankun*WANGYujunWANGJingxiao英文地址（The11thDepartmentChinesePeoplesLiberationArmyOfficerAcademyHefeiAnhui230031China英文摘要）Abstract：AlternatingDirectionMethodofMultipliers（ADMM）alreadyhassomepracticalapplicationsinmachinelearningfield.InordertoadapttothelargescaledataprocessingandnonsmoothlossconvexoptimizationproblemtheoriginalbatchADMMalgorithmwasimprovedbyusingmirrordescentmethodandanewcoordinateoptimizationalgorithmwasproposedforsolvingnonsmoothlossconvexoptimization.Thisnewalgorithmhasasimpleoperationandefficientcomputation.Throughdetailedtheoreticalanalysistheconvergenceofthenewalgorithmisverifiedanditalsohastheoptimalconvergencerateingeneralconvexcondition.Finallytheexperimentalresultscomparedwiththestateofartalgorithmsdemonstrateitgetsbetterconvergencerateunderthesparsityofsolution.AlternatingDirectionMethodofMultipliers（ADMM）alreadyhassomepracticalapplicationsinmachinelearningproblem.InordertoadapttothelargescaledataprocessingandnonsmoothlossconvexoptimizationproblemtheoriginalbatchADMMalgorithmhadbeenimprovedbyusingMirrorDescentmethodandproposedanewcoordinateoptimizationalgorithmforsolvingnonsmoothlossconvexoptimizationbaseonit.Thisnewalgorithmhasasimpleoperationandefficientcomputing.Throughdetailedtheoreticalana