New Lower Bounds for Private PAC Learning
Read the original on arXiv Machine Learning →The paper investigates realizable PAC learning under approximate differential privacy and develops a framework for establishing lower bounds on sample complexity. It demonstrates that classes sharing the same VC and Littlestone dimensions can have different private sample complexities, introducing the Independent Class Packing (ICP) parameter to capture this distinction. Using ICP, the authors derive tight lower bounds for several hypothesis classes, including axis-aligned rectangles, unions of intervals, linear subspaces, and improved bounds for halfspaces and convex polygons, and show that ICP characterizes private PAC sample complexity for product classes up to logarithmic factors.
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