Stochastic Trust-Region Methods for Over-parameterized Models

arXiv:2604.14017v1 Announce Type: cross Abstract: Under interpolation-type assumptions such as the strong growth condition, stochastic optimization methods can attain convergence rates comparable to full-batch methods, but their performance, particularly for SGD, remains highly sensitive to step-size selection. To address this issue, we propose a unified stochastic trust-region framework that eliminates manual step-size tuning and extends naturally to equality-constrained problems. For unconstrained optimization, we develop a first-order stochastic trust-region algorithm and show that, under the strong growth condition, it achieves an iteration and stochastic first-order oracle complexity of O(arepsilon^{-2} log(1/arepsilon)) for finding an arepsilon-stationary point. For equality-constrained problems, we introduce a quadratic-penalty-based stochastic trust-region method with penalty parameter mu, and establish an iteration and oracle complexity of O(arepsilon^{-4} log(1/arepsilon)) to reach an arepsilon-stationary point of the penalized problem, corresponding to an O(arepsilon)-approximate KKT point of the original constrained problem. Numerical experiments on deep neural network training and orthogonally constrained subspace fitting demonstrate that the proposed methods achieve performance comparable to well-tuned stochastic baselines, while exhibiting stable optimization behavior and effectively handling hard constraints without manual learning-rate scheduling.

Source: arXiv cs.LG | 2026-04-16