Stop Wasting My Gradients: Practical SVRG
We present and analyze several strategies for improving the performance of stochastic variance-reduced gradient (SVRG) methods. We first show that the convergence rate of these methods can be preserved under a decreasing sequence of errors in the control variate, and use this to derive variants of SVRG that use growing-batch strategies to reduce the number of gradient calculations required in the early iterations. We further (i) show how to exploit support vectors to reduce the number of gradient computations in the later iterations, (ii) prove that the commonly-used regularized SVRG iteration is justified and improves the convergence rate, (iii) consider alternate mini-batch selection strategies, and (iv) consider the generalization error of the method.
Comments:- Tricks like non-uniform sampling and then correcting by importance sampling have been around for much longer, see e.g. [1] which claims a speed-up of 3x. Those older approaches chose the probability based on error instead of L_i -- could you discuss/compare such an approach, at least in practice? I'd suspect this may be useful in practice where the L_i may not be known.- Channeling Leon Bottou: please discuss the limitations, and the cases where your method may *not* be applicable.- I would really appreciate an open-source code release accompanying the paper, which would increase its impact.- The experimental section and figures are clearly the weakest part of the paper, I'd recommend a serious second pass. For example, all plots should have error bars, state over how many runs they were averaged, labeled more clearly (SVRG -> full batch in top plots), the test-error plot does not have the resolution to be readable (maybe log-scale is better even if it won't go to zero). The same holds for the figures in the appendix. I do not understand why there is no difference at all between uniform sampling and Lipschitz sampling (in experiment 3)? Of course, a more challenging domain than logistic regression would be appreciated, but that can rightfully be shown in another paper. [1] Geoff Hinton, "To recognize objects, first learn to generate images", 2007.Typos:L19 a variant L53 increases over L77 expectation missing L96, L132 expectation symbol misformatted L164 B^s L289 can be used L316 superscript instead of subscript L325 sometimes L416 sometimes often?