Majorizing Measures for the Optimizer

@inproceedings{Borst2021MajorizingMF,
  title={Majorizing Measures for the Optimizer},
  author={Sander Borst and Daniel Dadush and Neil Olver and Makrand Sinha},
  booktitle={ITCS},
  year={2021}
}
The theory of majorizing measures, extensively developed by Fernique, Talagrand and many others, provides one of the most general frameworks for controlling the behavior of stochastic processes. In particular, it can be applied to derive quantitative bounds on the expected suprema and the degree of continuity of sample paths for many processes. One of the crowning achievements of the theory is Talagrand’s tight alternative characterization of the suprema of Gaussian processes in terms of… 
Generalization Properties of Stochastic Optimizers via Trajectory Analysis
TLDR
An encompassing theoretical framework for investigating the generalization properties of stochastic optimizers, which is based on their dynamics, and it is shown that both the Fernique–Talagrand functional and the local power-law exponent are predictive of generalization performance.

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