Stochastic Trust-Region Methods for Over-parameterized Models

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(varepsilon-2 log(1/varepsilon)) for finding an varepsilon-stationary point. For equality-constrained problems, we introduce a quadratic-penalty-based stochastic trust-region method with penalty parameter μ, and establish an iteration and oracle complexity of O(varepsilon-4 log(1/varepsilon)) to reach an varepsilon-stationary point of the penalized problem, corresponding to an O(varepsilon)-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.