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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper proposes a supervised learning algorithm. It uses stochastic gradient descent and periodically expands the hypothesis space by introducing new basis functions and adding corresponding components to the weight vector. As such, as it processes more data, it fits more complex models. The hypothesis space considered here are polynomials and higher order monomials are gradually introduced to the model. The concept of growing the hypothesis space as more data is introduced is not new (training kernel methods with SGD exhibits this behavior), but in the proposed method, choosing which monomials to add to the hypothesis space is very cheap.