基于高斯先验的Thompson采样的差分隐私
On The Differential Privacy of Thompson Sampling With Gaussian Prior
摘要：
我们表明，算法2（Agrawal & Goyal，2013）中详细描述的具有高斯先验的汤普森采样已经是差分私有的。定理1表明，在T轮后，它享有只有$\mathcal{O}(\ln^2 T)$的非常有竞争力的隐私损失。最后，定理2表明，通过适当增加高斯后验样本的方差，可以将隐私损失控制在任何期望的$ε$水平。而这只会增加一个术语$\mathcal{O}(\frac{\ln^2 T}ε)$的遗憾。这与文献中的汤普森采样的先前结果（（Mishra & Thakurta，2015））相比是有利的，该文献向遗憾添加了$\mathcal{O}(\frac{K \ln^3 T}{ε^2})$项以实现相同的隐私级别。此外，我们的结果使用了基本的汤普森采样，几乎没有修改，而（Mishra & Thakurta，2015）的结果需要复杂的构造。
英文摘要：
We show that Thompson Sampling with Gaussian Prior as detailed by Algorithm 2 in (Agrawal & Goyal, 2013) is already differentially private. Theorem 1 show that it enjoys a very competitive privacy loss of only $\mathcal{O}(\ln^2 T)$ after T rounds. Finally, Theorem 2 show that one can control the privacy loss to any desirable $ε$ level by appropriately increasing the variance of the samples from the Gaussian posterior. And this increases the regret only by a term of $\mathcal{O}(\frac{\ln^2 T}ε)$. This compares favorably to the previous result for Thompson Sampling in the literature ((Mishra & Thakurta, 2015)) which adds a term of $\mathcal{O}(\frac{K \ln^3 T}{ε^2})$ to the regret in order to achieve the same privacy level. Furthermore, our result use the basic Thompson Sampling with few modifications whereas the result of (Mishra & Thakurta, 2015) required sophisticated constructions.
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。
