arxiv:2610.11298

Nonminimizing Attractors of Stochastic Subgradient Methods on Semialgebraic Functions

Published on Oct 8

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Abstract

Stochastic subgradient methods can converge to nonminimizing critical points for semialgebraic functions, disproving a conjecture that subdifferential regularity is unnecessary for generic convergence to local minimizers.

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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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