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arXiv 2006.07503cs.LGstat.ML
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内隐在线学习的时间变异性

Temporal Variability in Implicit Online Learning

Università di Milano(米兰大学);Boston University(波士顿大学)

Nicolò Campolongo, Francesco Orabona

摘要:

在在线学习的背景下,隐式算法从实用的角度来看是非常成功的。然而,最严格的遗憾分析只显示了在线镜像下降的边际改善。在这项工作中,我们揭示了这种行为进行了仔细的遗憾分析。我们证明了一个新的静态遗憾界,依赖于时间的变化序列的损失函数,一个数量,这是经常遇到的考虑动态竞争对手。例如,我们表明,如果时间变异性是恒定的,并且学习率被适当地调整,而不需要平滑损失,则后悔可以是恒定的。此外,我们提出了一个自适应算法,实现了这个遗憾界的时间变化性的先验知识,并证明了一个匹配的下限。最后,我们在分类和回归数据集上验证了我们的理论发现。

英文摘要:

In the setting of online learning, Implicit algorithms turn out to be highly successful from a practical standpoint. However, the tightest regret analyses only show marginal improvements over Online Mirror Descent. In this work, we shed light on this behavior carrying out a careful regret analysis. We prove a novel static regret bound that depends on the temporal variability of the sequence of loss functions, a quantity which is often encountered when considering dynamic competitors. We show, for example, that the regret can be constant if the temporal variability is constant and the learning rate is tuned appropriately, without the need of smooth losses. Moreover, we present an adaptive algorithm that achieves this regret bound without prior knowledge of the temporal variability and prove a matching lower bound. Finally, we validate our theoretical findings on classification and regression datasets.

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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