ThreeOperatorSplittingwithaNonconvexLossFunctionAlpYurtsever1VarunMangalick1SuvritSra1Abstract2007),incertaintransportandassignmentproblems(Koop-mans&Beckmann,1957;Peyre´etal.,2019),amongcount-Wec...
UncertaintyquantificationforNonconvextensorcompletion:Confidenceintervals,heteroscedasticityandoptimalityChangxiaoCai1H.VincentPoor1YuxinChen1Abstractinformationabouttheunknowntensorplaysapivotalro...
StochasticGauss-NewtonAlgorithmsforNonconvexCompositionalOptimizationQuocTran-Dinh1NhanH.Pham1LamM.Nguyen2Abstractandnpi=1,thenbyintroductingFi(x):=i=1WedeveloptwonewstochasticGauss-Newtonalgorithm...
GuidedLearningofNonconvexModelsthroughSuccessiveFunctionalGradientOptimizationRieJohnson1TongZhang2AbstractOuroriginalmotivationwasfunctionalgradientlearningofadditivemodelsingradientboosting(Fried...
ComplexityofFindingStationaryPointsofNonsmoothNonconvexFunctionsJingzhaoZhang1HongzhouLin1StefanieJegelka1SuvritSra1AliJadbabaie1AbstractTable1.WhentheproblemisNonconvexandnonsmooth,find-inga-stati...
NonconvexVarianceReducedOptimizationwithArbitrarySamplingSamuelHorváth1PeterRichtárik123Abstractwherexcorrespondstotheparametersdefiningamodel,fi(x)isthelossofthemodelxassociatedwithdatapointWepr...
LowerBoundsforSmoothNonconvexFinite-SumOptimizationDongruoZhou1QuanquanGu1Abstractoffirst-orderalgorithmsforsolving(1.1),whichhaveac-cessestotheIncrementalFirst-orderOracle(IFO)(AgarwalSmoothfinite...
EfficientNonconvexRegularizedTensorCompletionwithStructure-awareProximalIterationsQuanmingYao12JamesT.Kwok2BoHan3AbstractInmanyapplications,onlyafewtensorentriesareob-served.Forexample,ofteneachYou...
AdaGradStepsizes:SharpConvergenceOverNonconvexLandscapesRachelWard12XiaoxiaWu12LéonBottou2AbstractcanbeapproximatedbytheaverageofalargenumberAdaptivegradientmethodssuchasAdaGradandnofcomponentfunc...
NonconvexOptimizationforRegressionwithFairnessConstraintsJunpeiKomiyama1AkikoTakeda12JunyaHonda12HajimeShimao3Abstractindefaultingonloans,directapplicationofmachinelearn-ingalgorithmwouldhighlylike...
ImplicitRegularizationinNonconvexStatisticalEstimation:GradientDescentConvergesLinearlyforPhaseRetrievalandMatrixCompletionCongMa1KaizhengWang1YuejieChi2YuxinChen3Abstract1.IntroductionRecentyearsh...
GraphicalNonconvexOptimizationviaanAdaptiveConvexRelaxationQiangSun1KeanMingTan2HanLiu3TongZhang3AbstractdiagonalmatrixwithdiagonalelementsofΣ∗.Itiswellknownthatthejthandkthvariablesareconditiona...
CovariateAdjustedPrecisionMatrixEstimationviaNonconvexOptimizationJinghuiChen1PanXu2LingxiaoWang2JianMa3QuanquanGu2Abstractassideinformationtoadjusttheestimationofprecisionmatrixcouldleadtobetterac...
AUnifiedVarianceReduction-BasedFrameworkforNonconvexLow-RankMatrixRecoveryLingxiaoWang1XiaoZhang1QuanquanGu1Abstractlaxationbasedoptimization(Srebroetal.,2004;Cande`s&Tao,2010;Rohdeetal.,2011;Recht...
NoSpuriousLocalMinimainNonconvexLowRankProblems:AUnifiedGeometricAnalysisRongGe1ChiJin2YiZheng1Abstract2016;Parketal.,2016)andmatrixcompletion(Geetal.,2016)havewell-behavedoptimizationlandscape:all...