Active Learning as Non-Convex Optimization

We propose a new view of active learning algorithms as optimization. We show that many online active learning algorithms can be viewed as stochastic gradient descent on non-convex objective functions. Variations of some of these algorithms and objective functions have been previously proposed without noting this connection. We also point out a connection between the standard min-margin offline active learning algorithm and non-convex losses. Finally, we discuss and show empirically how viewing active learning as non-convex loss minimization helps explain two previously observed phenomena: certain active learning algorithms achieve better generalization error than passive learning algorithms on certain data sets (Schohn and Cohn, 2000; Bordes et al., 2005) and on other data sets many active learning algorithms are prone to local minima (Schütze et al., 2006).