Fully Implicit Online Learning

09/25/2018

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by   Chaobing Song, et al.

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8

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Regularized online learning is widely used in machine learning. In this paper we analyze a class of regularized online algorithm with both non-linearized losses and non-linearized regularizers, which we call fully implicit online learning (FIOL). It is shown that because of avoiding the error of linearization, an extra additive regret gain can be obtained for FIOL. Then we show that by exploring the structure of the loss and regularizer, each iteration of FIOL can be exactly solved with time comparable to its linearized version, even if no closed-form solution exists. Experiments validate the proposed approaches.