AI 中文总结
该研究否定了Davis等人2026年的猜想，构造了二维半代数函数，证明随机次梯度方法可收敛到非极小Clarke临界点，为相关算法收敛性分析提供了反例。
AI 中文摘要
我们否定了Davis、Drusvyatskiy和Jiang（2026）的猜想，该猜想认为可从随机次梯度方法收敛到局部极小值的通用保证中移除次微分正则性。我们构造了一个二维的全局Lipschitz、强制半代数函数，对于合适的幂律步长，该方法会收敛到非极小的Clarke临界点，且这种收敛对初始点的开集、目标的线性倾斜均成立，在规定范围内的所有扰动序列上保持一致。
英文摘要
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.
Comments11 pages, 1 figure
