Stochastic Trust-Region Methods for Over-parameterized Models

• URL: http://arxiv.org/abs/2604.14017v1
• Date: Wed, 15 Apr 2026 15:57:34 GMT
• Title: Stochastic Trust-Region Methods for Over-parameterized Models
• Abstract summary: We propose a unified trust-region framework that eliminates manual step-size tuning and extends naturally to equality-constrained problems.<n>For unconstrained optimization, we develop a first-order trust-region algorithm and show that it achieves a first-order oracle complexity of $O(varepsilon-2 log (1/varepsilon)$ for finding an $varepsilon$-stationary point.<n>For equality-constrained problems, we introduce a quadratic-penalty-based trust-region method with penalty parameter $$, and establish an iteration and oracle complexity of $O(
• Score: 3.1231899978018824
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $O(\varepsilon^{-2} \log(1/\varepsilon))$ 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.

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