In many problem settings, for example on graph domains, online learning algorithms on streams of data need to respect strict time constraints dictated by the throughput on which the data arrive. When only a limited amount of memory (budget) is available, a learning algorithm will eventually need to discard some of the information used to represent the current solution, thus negatively affecting its classification performance. More importantly, the overhead due to budget management may significantly increase the computational burden of the learning algorithm. In this paper we present a novel approach inspired by the Passive Aggressive and the Lossy Counting algorithms. Our algorithm uses a fast procedure for deleting the less influential features. Moreover, it is able to estimate the weighted frequency of each feature and use it for prediction.