arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1906.09059cs.LGstat.ML
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用于对抗性比特预测的Thompson采样

Thompson Sampling for Adversarial Bit Prediction

Tel Aviv University(特拉维夫大学);Google Research(谷歌研究院)

Yuval Lewi, Haim Kaplan, Yishay Mansour

摘要:

我们研究了汤普森采样算法在对抗设置,特别是对抗比特预测。我们描述的位序列的最小和最大的预期遗憾。在具有$k < \frac{T}{2}$ 0的长度为$T$的序列中,最大遗憾的序列由交替的0和1以及随后的1组成,并且最小遗憾的序列由1以及随后的0组成。我们也限制了这些序列的遗憾,最坏情况序列有遗憾$O(\sqrt{T})$,最好情况序列有遗憾$O(1)$。我们将我们的结果扩展到假阳性和假阴性错误具有不同权重的模型。我们刻画了最大期望遗憾序列的特征,并推导出它们的遗憾界。我们还发现,有序列与$O(1)$遗憾。

英文摘要:

We study the Thompson sampling algorithm in an adversarial setting, specifically, for adversarial bit prediction. We characterize the bit sequences with the smallest and largest expected regret. Among sequences of length $T$ with $k < \frac{T}{2}$ zeros, the sequences of largest regret consist of alternating zeros and ones followed by the remaining ones, and the sequence of smallest regret consists of ones followed by zeros. We also bound the regret of those sequences, the worse case sequences have regret $O(\sqrt{T})$ and the best case sequence have regret $O(1)$. We extend our results to a model where false positive and false negative errors have different weights. We characterize the sequences with largest expected regret in this generalized setting, and derive their regret bounds. We also show that there are sequences with $O(1)$ regret.

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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