A proximal subgradient method for nonconvex stochastic optimization under the Kurdyka-Łojasiewicz condition

What the math gives to ML

The paper provides a constructive way to combine stochastic sample refinement, nonsmooth proximal updates, and Armijo-style backtracking without assuming weak convexity of the regularizer or a uniformly bounded stochastic-oracle variance. The transferable asset is the local sufficient-decrease guarantee for a proximal subgradient step: sufficiently small steps satisfy a quadratic decrease condition even when the empirical loss is nonconvex and nonsmooth. In neural-network training, this suggests an adaptive-batch proximal optimizer that increases batch size only when line-search tests are unreliable, rather than imposing a fixed batch-growth schedule. The method is especially suitable for exact proximal regularizers such as group sparsity, structured pruning, or hard parameter constraints.