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Stochastic Adaptive Quasi-Newton Methods for Minimizing Expected Values
Chaoxu Zhou · Wenbo Gao · Donald Goldfarb

Tue Aug 08 01:30 AM -- 05:00 AM (PDT) @ Gallery #17

We propose a novel class of stochastic, adaptive methods for minimizing self-concordant functions which can be expressed as an expected value. These methods generate an estimate of the true objective function by taking the empirical mean over a sample drawn at each step, making the problem tractable. The use of adaptive step sizes eliminates the need for the user to supply a step size. Methods in this class include extensions of gradient descent (GD) and BFGS. We show that, given a suitable amount of sampling, the stochastic adaptive GD attains linear convergence in expectation, and with further sampling, the stochastic adaptive BFGS attains R-superlinear convergence. We present experiments showing that these methods compare favorably to SGD.

Author Information

Chaoxu Zhou (Columbia University)
Wenbo Gao (Columbia University)
Donald Goldfarb (Columbia University)

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