On The Differential Privacy of Thompson Sampling With Gaussian Prior

Abstract

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 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). 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^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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