On The Differential Privacy of Thompson Sampling With Gaussian Prior
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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 O(^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 O(^2 T/ϵ). This compares favorably to the previous result for Thompson Sampling in the literature ((Mishra & Thakurta, 2015)) which adds a term of O(K ^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.
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