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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Summary: This paper proposes boosting algorithms and analyze them from an online learning perspective. First, they propose a boosting algorithm based on the update of the online mirror descent(MABoost). Then they show a smooth version of MABoost, i.e., a variant of MABoost which creates only smooth distributions over examples. Further, they propose sparse or lazy versions of MABoost and show their convergence proofs.