This paper presents a new, efficient method for learning task-specific word vectors using a variant of the Passive-Aggressive algorithm. Specifically, this algorithm learns a word embedding matrix in tandem with the classifier parameters in an online fashion, solving a bi-convex constrained optimization at each iteration. We provide a theoretical analysis of this new algorithm in terms of regret bounds, and evaluate it on both synthetic data and NLP classification problems, including text classification and sentiment analysis. In the latter case, we compare various pre-trained word vectors to initialize our word embedding matrix, and show that the matrix learned by our algorithm vastly outperforms the initial matrix, with performance results comparable or above the state-of-the-art on these tasks.