Finding Age Path of Self-Paced Learning

Self-paced learning (SPL) is an emerging research topic in recent machine learning research which is often formulated as a bi-convex problem. The choice of the age parameter in SPL can control the learning pace and is crucial to achieve optimal performance. Traditionally, the age parameter is programmed to increase in a fixed rate while solving the SPL problem using the alternative optimization strategy (AOS). However, this simple heuristic is likely to miss the optimal age parameter especially when efficiency is a major concern. To address this problem, we propose a solution path method, APSPL, which can track the optimal solutions of SPL with respect to the change of age parameter (age path). Specifically, we use the difference of convex (DC) formulation to replace the original biconvex problem, which enables us to derive the path-following algorithm. For better efficiency, our algorithm uses a decremental and incremental training strategy to avoid retraining several times at different age values. We theoretically prove that the solutions produced by APSPL are the same as those generated by traditional SPL solvers. We also provide the finite time convergence proof of APSPL. To demonstrate the applicability of APSPL, we provide an extension of APSPL for semi-supervised classification. To the best of our knowledge, APSPL is the first solution path algorithm for self-paced learning. Experimental results on a variety of benchmark datasets not only verify the effectiveness and efficiency of APSPL over traditional SPL, but also show the advantage of using the optimal age parameter.