Self-Paced Curriculum Learning

Curriculum learning (CL) or self-paced learning (SPL) represents a recently proposed learning regime inspired by the learning process of humans and animals that gradually proceeds from easy to more complex samples in training. The two methods share a similar conceptual learning paradigm, but differ in specific learning schemes. In CL, the curriculum is predetermined by prior knowledge, and remain fixed thereafter. Therefore, this type of method heavily relies on the quality of prior knowledge while ignoring feedback about the learner. In SPL, the curriculum is dynamically determined to adjust to the learning pace of the leaner. However, SPL is unable to deal with prior knowledge, rendering it prone to overfitting. In this paper, we discover the missing link between CL and SPL, and propose a unified framework named self-paced curriculum leaning (SPCL). SPCL is formulated as a concise optimization problem that takes into account both prior knowledge known before training and the learning progress during training. In comparison to human education, SPCL is analogous to “instructor-student-collaborative” learning mode, as opposed to “instructor-driven” in CL or “student-driven” in SPL. Empirically, we show that the advantage of SPCL on two tasks. Curriculum learning (Bengio et al. 2009) and self-paced learning (Kumar, Packer, and Koller 2010) have been attracting increasing attention in the field of machine learning and artificial intelligence. Both the learning paradigms are inspired by the learning principle underlying the cognitive process of humans and animals, which generally start with learning easier aspects of a task, and then gradually take more complex examples into consideration. The intuition can be explained in analogous to human education in which a pupil is supposed to understand elementary algebra before he or she can learn more advanced algebra topics. This learning paradigm has been empirically demonstrated to be instrumental in avoiding bad local minima and in achieving a better generalization result (Khan, Zhu, and Mutlu 2011; Basu and Christensen 2013; Tang et al. 2012). A curriculum determines a sequence of training samples which essentially corresponds to a list of samples ranked in ascending order of learning difficulty. A major disparity Copyright c © 2015, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. between curriculum learning (CL) and self-paced learning (SPL) lies in the derivation of the curriculum. In CL, the curriculum is assumed to be given by an oracle beforehand, and remains fixed thereafter. In SPL, the curriculum is dynamically generated by the learner itself, according to what the learner has already learned. The advantage of CL includes the flexibility to incorporate prior knowledge from various sources. Its drawback stems from the fact that the curriculum design is determined independently of the subsequent learning, which may result in inconsistency between the fixed curriculum and the dynamically learned models. From the optimization perspective, since the learning proceeds iteratively, there is no guarantee that the predetermined curriculum can even lead to a converged solution. SPL, on the other hand, formulates the learning problem as a concise biconvex problem, where the curriculum design is embedded and jointly learned with model parameters. Therefore, the learned model is consistent. However, SPL is limited in incorporating prior knowledge into learning, rendering it prone to overfitting. Ignoring prior knowledge is less reasonable when reliable prior information is available. Since both methods have their advantages, it is difficult to judge which one is better in practice. In this paper, we discover the missing link between CL and SPL. We formally propose a unified framework called Self-paced Curriculum Leaning (SPCL). SPCL represents a general learning paradigm that combines the merits from both the CL and SPL. On one hand, it inherits and further generalizes the theory of SPL. On the other hand, SPCL addresses the drawback of SPL by introducing a flexible way to incorporate prior knowledge. This paper also discusses concrete implementations within the proposed framework, which can be useful for solving various problems. This paper offers a compelling insight on the relationship between the existing CL and SPL methods. Their relation can be intuitively explained in the context of human education, in which SPCL represents an “instructor-student collaborative” learning paradigm, as opposed to “instructordriven” in CL or “student-driven” in SPL. In SPCL, instructors provide prior knowledge on a weak learning sequence of samples, while leaving students the freedom to decide the actual curriculum according to their learning pace. Since an optimal curriculum for the instructor may not necessarily be optimal for all students, we hypothesize that given reasonable prior knowledge, the curriculum devised by instructors and students together can be expected to be better than the curriculum designed by either part alone. Empirically, we substantiate this hypothesis by demonstrating that the proposed method outperforms both CL and SPL on two tasks. The rest of the paper is organized as follows. We first briefly introduce the background knowledge on CL and SPL. Then we propose the model and the algorithm of SPCL. After that, we discuss concrete implementations of SPCL. The experimental results and conclusions are presented in the last two sections. Background Knowledge