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About this paper
Shashaank Aiyer, Yishay Mansour, Shay Moran, Han Shao, Tom Waknine
The authors establish a scale-sensitive equivalence between uniform convergence, agnostic learning, and fat-shattering dimension for bounded real-valued function classes. They construct empirical covers directly to avoid the scale loss of packing-based arguments, improving a sample-complexity bound from Õ(d/ε³) to Õ(d/ε²). For bounded IPMs, infinite fat-shattering at a scale in (0, 1/2) yields optimal 3-weak evaluability, a theoretical result, not a generator experiment.
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