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Based on differential privacy (DP) framework, we introduce and unify privacydefinitions for the multi-armed bandit algorithms. We represent the frameworkwith a unified graphical model and use it to connect privacy definitions. Wederive and contrast lower bounds on the regret of bandit algorithms satisfyingthese definitions. We leverage a unified proving technique to achieve all thelower bounds. We show that for all of them, the learner's regret is increasedby a multiplicative factor dependent on the privacy level $\epsilon$. Weobserve that the dependency is weaker when we do not require local differentialprivacy for the rewards.

Differential Privacy for Multi-armed Bandits: What Is It and What Is Its Cost?