Bandit Multiclass Linear Classification: Efficient Algorithms for the Separable Case
International Conference on Machine Learning(2019)
摘要
We study the problem of efficient online multiclass linear classification with bandit feedback, where all examples belong to one of K classes and lie in the d-dimensional Euclidean space. Previous works have left open the challenge of designing efficient algorithms with finite mistake bounds when the data is linearly separable by a margin 'y. In this work, we take a first step towards this problem. We consider two notions of linear separability, strong and weak. 1. Under the strong linear separability condition, we design an efficient algorithm that achieves a near-optimal mistake bound of O (K/gamma(2)). 2. Under the more challenging weak linear separability condition, we design an efficient algorithm with a mistake bound of min (2((O) over tilde (K log2(1/gamma))), 2((O) over bar(root 1/gamma log K)))(1). Our algorithm is based on kernel Perceptron and is inspired by the work of Klivans & Servedio (2008) on improperly learning intersection of halfspaces.
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