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Non-interactive Local Differential Privacy (LDP) requires data analysts tocollect data from users through noisy channel at once. In this paper, we extendthe frontiers of Non-interactive LDP learning and estimation from severalaspects. For learning with smooth generalized linear losses, we propose anapproximate stochastic gradient oracle estimated from non-interactive LDPchannel, using Chebyshev expansion. Combined with inexact gradient methods, weobtain an efficient algorithm with quasi-polynomial sample complexity bound.For the high-dimensional world, we discover that under $\ell_2$-norm assumptionon data points, high-dimensional sparse linear regression and mean estimationcan be achieved with logarithmic dependence on dimension, using randomprojection and approximate recovery. We also extend our methods to Kernel RidgeRegression. Our work is the first one that makes learning and estimationpossible for a broad range of learning tasks under non-interactive LDP model.

Collect at Once, Use Effectively: Making Non-interactive Locally Private Learning Possible