Abstract

We study the fundamental problem of learning an unknown large-margin halfspace in the context of parallel computation. Our main positive result is a parallel algorithm for learning a large-margin halfspace that is based on interior point methods from convex optimization and fast parallel algorithms for matrix computations. We show that this algorithm learns an unknown -margin halfspace over n dimensions using processors and runs in time In contrast, naive parallel algorithms that learn a -margin halfspace in time that depends polylogarithmically on n have runtime dependence on . Our main negative result deals with boosting, which is a standard approach to learning large-margin halfspaces. We give an information-theoretic proof that in the original PAC framework, in which a weak learning algorithm is provided as an oracle that is called by the booster, boosting cannot be parallelized: the ability to call the weak learner multiple times in parallel within a single boosting stage does not reduce the overall number of successive stages of boosting that are required.