On the Uniform Convergence of Subdifferentials in Stochastic Optimization and Learning

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Analysis reveals uniform convergence rates for subdifferentials in stochastic optimization, highlighting implications for risk approximation.

Uniform convergence of subdifferentials can clarify how empirical points approximate population ones, offering new insights in optimization.
The study shows that a uniform bound on convergence of subgradients leads to a uniform bound on Hausdorff distance between subdifferentials.
Using a proposed reduction principle, it simplifies set-valued convergence to vector-valued convergence for stochastic objectives.
Findings provide guarantees in stochastic convex-composite optimization without needing differentiability of population risks.

Feng Ruan (2025) studied this question.

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Analysis reveals uniform convergence rates for subdifferentials in stochastic optimization, highlighting implications for risk approximation.