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Department of Mathematics,
Department of Mathematics,
University of California San Diego
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Math 278B: Mathematics of Information, Data, and Signals
Lai Tian
USC
Failure of uniform laws of large numbers for subdifferentials and beyond
Abstract:
We provide counterexamples showing that uniform laws of large numbers do not hold for subdifferentials under modest assumptions. Our results apply to random Lipschitz, convex, and convex-composite functions with randomness confined to the inner smooth map. Consequently, they resolve in the negative the questions posed by Shapiro and Xu [J. Math. Anal. Appl., 325(2), 2007] and highlight the obstacles nonsmoothness poses to uniform results.
November 7, 2025
11:00 AM
APM 6402
Research Areas
Mathematics of Information, Data, and Signals****************************
