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Compositional Stochastic Average Gradient for Machine Learning and Related Applications
Many machine learning, statistical inference, and portfolio optimization
problems require minimization of a composition of expected value functions
(CEVF). Of particular interest is the finite-sum versions of such compositional
optimization problems (FS-CEVF). Compositional stochastic variance reduced
gradient (C-SVRG) methods that combine stochastic compositional gradient
descent (SCGD) and stochastic variance reduced gradient descent (SVRG) methods
are the state-of-the-art methods for FS-CEVF problems. We introduce
compositional stochastic average gradient descent (C-SAG) a novel extension of
the stochastic average gradient method (SAG) to minimize composition of
finite-sum functions. C-SAG, like SAG, estimates gradient by incorporating
memory of previous gradient information. We present theoretical analyses of
C-SAG which show that C-SAG, like SAG, and C-SVRG, achieves a linear
convergence rate when the objective function is strongly convex; However, C-CAG
achieves lower oracle query complexity per iteration than C-SVRG. Finally, we
present results of experiments showing that C-SAG converges substantially
faster than full gradient (FG), as well as C-SVRG