In this paper, we study the mistake bound of online kernel learning on a budget. We propose a new budgeted online kernel learning model, called Ahpatron, which significantly improves the mistake bound of previous work and resolves the open problem posed by Dekel, Shalev-Shwartz, and Singer (2005). We first present an aggressive variant of Perceptron, named AVP, a model without budget, which uses an active updating rule. Then we design a new budget maintenance mechanism, which removes a half of examples,and projects the removed examples onto a hypothesis space spanned by the remaining examples. Ahpatron adopts the above mechanism to approximate AVP. Theoretical analyses prove that Ahpatron has tighter mistake bounds, and experimental results show that Ahpatron outperforms the state-of-the-art algorithms on the same or a smaller budget.

翻译：本文研究了预算约束下的在线核学习错误边界问题。我们提出了一种新的预算在线核学习模型——Ahpatron，该模型显著改进了前人工作的错误边界，并解决了Dekel、Shalev-Shwartz和Singer（2005）提出的开放性问题。首先，我们提出感知机的激进变体AVP（无预算模型），该模型采用主动更新规则。随后设计了一种新的预算维护机制：移除半数样本，并将被移除样本投影到剩余样本张成的假设空间。Ahpatron采用上述机制近似AVP。理论分析证明Ahpatron具有更紧的错误边界，实验结果表明，在相同或更小预算下，Ahpatron性能优于当前最先进算法。