Online Passive-Aggressive Algorithms on a Budget
Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:908-915, 2010.
In this paper a kernel-based online learning algorithm, which has both constant space and update time, is proposed. The approach is based on the popular online Passive-Aggressive (PA) algorithm. When used in conjunction with kernel function, the number of support vectors in PA grows without bounds when learning from noisy data streams. This implies unlimited memory and ever increasing model update and prediction time. To address this issue, the proposed budgeted PA algorithm maintains only a fixed number of support vectors. By introducing an additional constraint to the original PA optimization problem, a closed-form solution was derived for the support vector removal and model update. Using the hinge loss we developed several budgeted PA algorithms that can trade between accuracy and update cost. We also developed the ramp loss versions of both original and budgeted PA and showed that the resulting algorithms can be interpreted as the combination of active learning and hinge loss PA. All proposed algorithms were comprehensively tested on 7 benchmark data sets. The experiments showed that they are superior to the existing budgeted online algorithms. Even with modest budgets, the budgeted PA achieved very competitive accuracies to the non-budgeted PA and kernel perceptron algorithms.