Open Problems in Efficient Semi-Supervised PAC Learning

The standard PAC model focuses on learning a class of functions from labeled examples, where the two critical resources are the number of examples needed and running time. In many natural learning problems, however, unlabeled data can be obtained much more cheaply than labeled data. This has motivated the notion of semi-supervised learning, in which algorithms attempt to use this cheap unlabeled data in a way that (hopefully) reduces the number of labeled examples needed for learning [4]. For instance, semi-supervised and transductive SVM [2,5] and co-training [3] are two examples of semi-supervised learning algorithms. In [1], a semi-supervised PAC model is introduced that provides a common framework for the kinds of assumptions these algorithms make; however, most of the results in [1] deal with sample complexity rather than computational efficiency, or are only computationally efficient under strong assumptions on the underlying distribution. This note poses several questions related to developing computationally efficient algorithms in this semi-supervised PAC model.