Compared with conventional minimization problems (e.g., empirical risk minimization), min-max optimization has aricher mathematical structure, thus being able tomodel more sophisticated learning problems thatemergefrom ever-emerging applications.

Indeedin learning applications, where symmetric tensors areformed from statistical moments (higher-order covariances) or multivariate derivatives (higher-order Hessians), CP decomposition has enabled parameter estimation for mixtures of Gaussians [20, 35], generalized linear models [34], shallow neuralnetworks[19,24,42],deepernetworks[17,18,30],hiddenMarkovmodels[5],amongothers.