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Empirical Risk Minimization in Non-interactive Local Differential Privacy Revisited

Neural Information Processing Systems

In this paper, we revisit the Empirical Risk Minimization problem in the noninteractive local model of differential privacy. In the case of constant or low dimensions (pn), we first show that if the loss function is(,T)-smooth, wecanavoidadependence ofthesample complexity,toachieveerrorα,onthe exponential of the dimensionalityp with base1/α (i.e.,α p), which answers a questionin[19].