Generalization Guarantees of Randomized Block Coordinate Descent for Nonconvex Learning
Read the original on arXiv Machine Learning →The paper presents high‑probability generalization guarantees for Randomized Block Coordinate Descent (RBCD) when applied to nonconvex learning problems. It derives bounds on the gradients of both empirical and population risks under standard smoothness assumptions, and shows how polynomially decaying step sizes and early stopping can achieve optimal convergence rates for population gradients. In settings where the objective is gradient‑dominated, the authors provide functional suboptimality bounds that approach optimistic rates seen in convex or low‑noise scenarios, and they also establish dimension‑independent bounds for loss functions with a particular structure, extending applicability to high‑dimensional problems.
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