Large Margin Classification for Moving Targets

We consider using online large margin classification algorithms in a setting where the target classifier may change over time. The algorithms we consider are Gentile's ALMA, and an algorithm we call NORMA which performs a modified online gradient descent with respect to a regularised risk. The update rule of ALMA includes a projection-based regularisation step, whereas NORMA has a weight decay type of regularisation. For ALMA we can prove mistake bounds in terms of the total distance the target moves during the trial sequence. For NORMA, we need the additional assumption that the movement rate stays sufficiently low uniformly over time. In addition to the movement of the target, the mistake bounds for both algorithms depend on the hinge loss of the target. Both algorithms use a margin parameter which can be tuned to make them mistake-driven (update only when classification error occurs) or more aggressive (update when the confidence of the classification is below the margin). We get similar mistake bounds both for the mistake-driven and a suitable aggressive tuning. Experiments on artificial data confirm that an aggressive tuning is often useful even if the goal is just to minimise the number of mistakes.