On the Computational Power of Online Gradient Descent

07/03/2018

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by   Vaggos Chatziafratis, et al.

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We prove that the evolution of weight vectors in online gradient descent can encode arbitrary polynomial-space computations, even in the special case of soft-margin support vector machines. Our results imply that, under weak complexity-theoretic assumptions, it is impossible to reason efficiently about the fine-grained behavior of online gradient descent.