Thompson Sampling Itself is Differentially Private

TL;DR

This paper demonstrates that the classical Thompson sampling algorithm for multi-armed bandits inherently provides differential privacy guarantees without modification, and explores simple adjustments to enhance privacy while maintaining low regret.

Contribution

It proves the inherent differential privacy of Thompson sampling and introduces simple modifications to improve privacy-utility tradeoffs with theoretical and empirical validation.

Findings

Thompson sampling is differentially private without changes.

Simple modifications can tighten privacy guarantees.

Tuning parameters improves privacy-regret balance.

Abstract

In this work we first show that the classical Thompson sampling algorithm for multi-arm bandits is differentially private as-is, without any modification. We provide per-round privacy guarantees as a function of problem parameters and show composition over $T$ rounds; since the algorithm is unchanged, existing $O(\sqrt{NT\log N})$ regret bounds still hold and there is no loss in performance due to privacy. We then show that simple modifications -- such as pre-pulling all arms a fixed number of times, increasing the sampling variance -- can provide tighter privacy guarantees. We again provide privacy guarantees that now depend on the new parameters introduced in the modification, which allows the analyst to tune the privacy guarantee as desired. We also provide a novel regret analysis for this new algorithm, and show how the new parameters also impact expected regret. Finally, we empirically validate and illustrate our theoretical findings in two parameter regimes and demonstrate that tuning the new parameters substantially improve the privacy-regret tradeoff.