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Self-paced learning (SPL) is a new methodology that simulates the learningprinciple of humans/animals to start learning easier aspects of a learningtask, and then gradually take more complex examples into training. Thisnew-coming learning regime has been empirically substantiated to be effectivein various computer vision and pattern recognition tasks. Recently, it has beenproved that the SPL regime has a close relationship to a implicit self-pacedobjective function. While this implicit objective could provide helpfulinterpretations to the effectiveness, especially the robustness, insights underthe SPL paradigms, there are still no theoretical results strictly proved toverify such relationship. To this issue, in this paper, we provide someconvergence results on this implicit objective of SPL. Specifically, we provethat the learning process of SPL always converges to critical points of thisimplicit objective under some mild conditions. This result verifies theintrinsic relationship between SPL and this implicit objective, and makes theprevious robustness analysis on SPL complete and theoretically rational.

On Convergence Property of Implicit Self-paced Objective