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Nonminimizing Attractors of Stochastic Subgradient Methods on Semialgebraic Functions
Abstract
We disprove a conjecture of Davis, Drusvyatskiy, and Jiang (2026) that subdifferential regularity can be removed from the generic guarantee of convergence to local minimizers for stochastic subgradient methods. We construct a globally Lipschitz, coercive, semialgebraic function in two dimensions for which the method converges to a nonminimizing Clarke critical point. For suitable power-law stepsizes, this convergence holds for open sets of initial points and linear tilts of the objective, uniformly over all perturbation sequences within a prescribed bound.
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BibTeX
@misc{li2026nonminimizing,
title = {{Nonminimizing Attractors of Stochastic Subgradient Methods on Semialgebraic Functions}},
author = {Jiajin Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11298},
eprint = {2610.11298},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11298},
}
RIS
TY - UNPB
TI - Nonminimizing Attractors of Stochastic Subgradient Methods on Semialgebraic Functions
AU - Jiajin Li
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11298
UR - https://arxiv.org/abs/2610.11298
AB - We disprove a conjecture of Davis, Drusvyatskiy, and Jiang (2026) that subdifferential regularity can be removed from the generic guarantee of convergence to local minimizers for stochastic subgradient methods. We construct a globally Lipschitz, coercive, semialgebraic function in two dimensions for which the method converges to a nonminimizing Clarke critical point. For suitable power-law stepsizes, this convergence holds for open sets of initial points and linear tilts of the objective, uniformly over all perturbation sequences within a prescribed bound.
ER -