By batching losses and using heavy-tailed bandit algorithms, any non-private adversarial bandit algorithm can be made epsilon-differentially private with regret O(sqrt(KT)/sqrt(epsilon)), and the first private expert-advice algorithms are given.
The price of differential privacy for online learning
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Faster Rates for Private Adversarial Bandits
By batching losses and using heavy-tailed bandit algorithms, any non-private adversarial bandit algorithm can be made epsilon-differentially private with regret O(sqrt(KT)/sqrt(epsilon)), and the first private expert-advice algorithms are given.