  This paper investigates the problem of regret minimization for multi-armed
bandit (MAB) problems with local differential privacy (LDP) guarantee. Given a
fixed privacy budget $\epsilon$, we consider three privatizing mechanisms under
Bernoulli scenario: linear, quadratic and exponential mechanisms. Under each
mechanism, we derive stochastic regret bound for Thompson Sampling algorithm.
Finally, we simulate to illustrate the convergence of different mechanisms
under different privacy budgets.
