A natural idea is to compute the solution path w.r.t.

Nowadays self-paced learning (SPL) is an important machine learning paradigm that mimics the cognitive process of humans and animals. The SPL regime involves a self-paced regularizer and a gradually increasing age parameter, which plays a key role in SPL but where to optimally terminate this process is still non-trivial to determine. A natural idea is to compute the solution path w.r.t. age parameter (i.e., age-path). However, current age-path algorithms are either limited to the simplest regularizer, or lack solid theoretical understanding as well as computational efficiency. To address this challenge, we propose a novel \underline{G}eneralized \underline{Ag}e-path \underline{A}lgorithm (GAGA) for SPL with various self-paced regularizers based on ordinary differential equations (ODEs) and sets control, which can learn the entire solution spectrum w.r.t. a range of age parameters. To the best of our knowledge, GAGA is the first exact path-following algorithm tackling the age-path for general self-paced regularizer. Finally the algorithmic steps of classic SVM and Lasso are described in detail. We demonstrate the performance of GAGA on real-world datasets, and find considerable speedup between our algorithm and competing baselines.

By simulating the easy-to-hard learning manners of humans/animals, the learning regimes called curriculum learning~(CL) and self-paced learning~(SPL) have been recently investigated and invoked broad interests. However, the intrinsic mechanism for analyzing why such learning regimes can work has not been comprehensively investigated. To this issue, this paper proposes a concave conjugacy theory for looking into the insight of CL/SPL. Specifically, by using this theory, we prove the equivalence of the SPL regime and a latent concave objective, which is closely related to the known non-convex regularized penalty widely used in statistics and machine learning. Beyond the previous theory for explaining CL/SPL insights, this new theoretical framework on one hand facilitates two direct approaches for designing new SPL models for certain tasks, and on the other hand can help conduct the latent objective of self-paced curriculum learning, which is the advanced version of both CL/SPL and possess advantages of both learning regimes to a certain extent. This further facilitates a theoretical understanding for SPCL, instead of only CL/SPL as conventional. Under this theory, we attempt to attain intrinsic latent objectives of two curriculum forms, the partial order and group curriculums, which easily follow the theoretical understanding of the corresponding SPCL regimes.

It is known that Boosting can be interpreted as a gradient descent technique to minimize an underlying loss function. Specifically, the underlying loss being minimized by the traditional AdaBoost is the exponential loss, which is proved to be very sensitive to random noise/outliers. Therefore, several Boosting algorithms, e.g., LogitBoost and SavageBoost, have been proposed to improve the robustness of AdaBoost by replacing the exponential loss with some designed robust loss functions. In this work, we present a new way to robustify AdaBoost, i.e., incorporating the robust learning idea of Self-paced Learning (SPL) into Boosting framework. Specifically, we design a new robust Boosting algorithm based on SPL regime, i.e., SPLBoost, which can be easily implemented by slightly modifying off-the-shelf Boosting packages. Extensive experiments and a theoretical characterization are also carried out to illustrate the merits of the proposed SPLBoost.