arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2007.12618cs.LGmath.OCstat.ML
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在线多类分类中的代理间隙利用

Exploiting the Surrogate Gap in Online Multiclass Classification

Leiden University(莱顿大学)

Dirk van der Hoeven

摘要:

我们提出了Gaptron,一个随机的一阶在线多类分类算法。在充分的信息设置中,我们显示预期的错误界相对于逻辑损失,铰链损失,和平滑铰链损失与不断遗憾,其中的期望是相对于学习者的随机性。在强盗分类设置,我们表明,Gaptron是第一个线性时间算法与$O(K\sqrt{T})$预期遗憾,其中$K$是类的数量。此外,Gaptron的预期错误界不依赖于特征向量的维数,与以前的算法$O(K\sqrt{T})$遗憾的强盗分类设置。我们提出了一种新的证明技术,利用零-一损失和代理损失之间的差距,而不是利用属性,如指数或混合性,这是传统上用于证明对数或常数遗憾界。

英文摘要:

We present Gaptron, a randomized first-order algorithm for online multiclass classification. In the full information setting we show expected mistake bounds with respect to the logistic loss, hinge loss, and the smooth hinge loss with constant regret, where the expectation is with respect to the learner's randomness. In the bandit classification setting we show that Gaptron is the first linear time algorithm with $O(K\sqrt{T})$ expected regret, where $K$ is the number of classes. Additionally, the expected mistake bound of Gaptron does not depend on the dimension of the feature vector, contrary to previous algorithms with $O(K\sqrt{T})$ regret in the bandit classification setting. We present a new proof technique that exploits the gap between the zero-one loss and surrogate losses rather than exploiting properties such as exp-concavity or mixability, which are traditionally used to prove logarithmic or constant regret bounds.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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