The Price of Differential Privacy for Online Learning
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Abstract
We design differentially private algorithms for the problem of online linear optimization in the fullpinformation and bandit settings with optimal 
regret bounds. In the full-information setting, our results demonstrate that "-different privacy may be ensured for free p – in particula the regret bounds scale as 
For bandit linear optimization, and as a special case for non-stochastic multi-armed bandits,?the prop posed algorithm achieves a regret of 
while the previously known best regret bound was 
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