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A Geometric View of Non-Linear On-Line Stochastic Gradient Descent

We investigate a relationship between geometric structure of a parameter space and on-line learning algorithms. The geometric structure is often implied by a nature of a problem to be solved. For example, the parameters one wishes to learn are a subject to constrains, or they are intrinsically non-linear objects or they are distributed in a non uniform, but known way. We develop a mistake bound analysis for a two new geometric algorithms and show that link functions based algorithms are essentially the transformed geometric algorithms.