A Mosco sufficient condition for intrinsic stability of non-unique convex Empirical Risk Minimization
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Abstract (arXiv)
Empirical risk minimization (ERM) stability is usually studied via single-valued outputs, while convex non-strict losses yield set-valued minimizers. We identify Painlev'e-Kuratowski upper semicontinuity (PK-u.s.c.) as the intrinsic stability notion for the ERM solution correspondence (set-level Hadamard well-posedness) and a prerequisite to interpret stability of selections. We then characterize a minimal non-degenerate qualitative regime: Mosco-consistent perturbations and locally bounded minimizers imply PK-u.s.c., minimal-value continuity, and consistency of vanishing-gap near-minimizers. Quadratic growth yields explicit quantitative deviation bounds.
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References · 5
- 2016Understanding deep learning requires rethinking generalizationcited by 1,657
- 2018Reconciling modern machine learning practice and the bias-variance trade-offcited by 919
- 2017The Implicit Bias of Gradient Descent on Separable Datacited by 649
- 2020Improving Reproducibility in Machine Learning Research (A Report from the NeurIPS 2019 Reproducibility Program)cited by 318
- 2015Norm-Based Capacity Control in Neural Networkscited by 299
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