On The Differential Privacy of Thompson Sampling With Gaussian Prior notes

这是arxiv上的一个占坑文吧。好像也没有写出后续。

Tossou A C Y, Dimitrakakis C. On The Differential Privacy of Thompson Sampling With Gaussian Prior[J]. arXiv preprint arXiv:1806.09192, 2018.

主要结论是说基于高斯先验的TS算法 ([1]中的算法2) 已经是满足DP的。

理论1表明T轮迭代后的privacy loss是$O(\ln^2 T)$的。

理论2表明可以通过调整高斯后验的方差来控制privacy loss的level。

Thompson Sampling is a randomized algorithm that works in a Bayesian framework.

Reference

[1] Agrawal, Shipra and Goyal, Navin. Further optimal regret bounds for thompson sampling. In Artificial Intelligence and Statistics, pp. 99–107, 2013.