Researchers have designed differentially private algorithms for prediction with expert advice under dynamic regret.
The algorithms address three types of adversaries: stochastic with shifting distributions, oblivious, and adaptive.
For the shifting stochastic adversary, the algorithm achieves expected dynamic regret of at most O(sqrt(STlog(NT)) + (Slog(NT)/ε)), where S is the number of distribution shifts, T is the horizon, and N is the number of experts.
The research shows a fundamental separation between oblivious and adaptive adversaries, with sub-linear regret achievable for oblivious adversaries in the high-privacy regime, but linear dynamic regret inevitable under adaptive adversaries.