A Unified Framework for Bandit Online Multiclass Prediction

Bandit online multiclass prediction plays an important role in many real-world applications. In this paper, we propose a unified Bandit Online Multiclass Prediction (BOMP) framework. This framework is based on our proposed margin-based gradient descent approach. Its update step provides an unbiased estimate of the surrogate loss gradient and has a lower variance than existing methods. It also enables our algorithms to update even for incorrect predictions by penalizing the wrong classes. The link function of the framework can evolve over time, gradually incorporating online data information including second-order information into the potential functions. Based on the proposed framework, we investigate first-order and second-order bandit online multiclass prediction algorithms. Theoretical analysis demonstrates the superiority of our proposed update rule and bandit online multiclass prediction framework. Finally, we compare our proposed first-order and second-order bandit online multiclass prediction algorithms with several state-of-the-art methods on two synthetic and four real-world datasets. The encouraging results show that our proposed algorithms significantly outperform state-of-the-art techniques.