The Price of Differential Privacy for Online Learning

We design differentially private algorithms for the problem of online linear optimization in the full information and bandit settings with optimal (O) over tilde(root T)(1) regret bounds. In the full-information setting, our results demonstrate that epsilon-differential privacy may be ensured for free - in particular, the regret bounds scale as O(root T) + (O) over tilde (1/epsilon). For bandit linear optimization, and as a special case, for non-stochastic multi-armed bandits, the pro- posed algorithm achieves a regret of (O) over tilde (1/epsilon root T) , while the previously known best regret bound was (O) over tilde (1/epsilon T-2/3).