发表机构
Georgia Institute of Technology; University of California, Berkeley（佐治亚理工学院; 加州大学伯克利分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对重尾噪声下带等式约束的随机优化，提出基于随机序列二次规划框架的信赖域方法TR-SSQP，采用法向-切向分解和归一化半径及Polyak动量，实现全局几乎必然收敛，并通过数值实验验证性能。
AI 中文摘要
我们考虑具有确定性等式约束的随机非线性优化问题。虽然无约束随机优化已被充分研究，但在约束设置中，最优性与可行性的相互作用带来了重大挑战。此外，现有约束随机方法的理论保证主要依赖于有界方差假设，使得重尾噪声机制在很大程度上未被探索。为解决这一空白，我们提出了一种在随机序列二次规划框架内的新型信赖域方法，称为TR-SSQP。我们的方法在步长计算中采用法向-切向分解以平衡最优性与可行性。此外，我们在信赖域半径的设计中引入归一化机制，并结合用于梯度估计的Polyak动量，确保无需梯度裁剪即可实现稳定更新。当信赖域半径和动量参数以适当速率衰减时，我们建立了该方法的全局几乎必然收敛性。据我们所知，这是重尾噪声下约束随机优化的首个渐近收敛结果。我们通过大量数值实验展示了所提出方法的良好性能，包括其变体之间以及与现有约束随机优化方法的比较。
英文摘要
We consider stochastic nonlinear optimization problems with deterministic equality constraints. While unconstrained stochastic optimization is well understood, the interplay between optimality and feasibility in the constrained setting poses significant challenges. Moreover, existing theoretical guarantees for constrained stochastic methods predominantly rely on bounded-variance assumptions, leaving the heavy-tailed noise regime largely unexplored. To address this gap, we propose a novel trust-region method within the stochastic sequential quadratic programming framework, termed TR-SSQP. Our method employs a normal-tangential decomposition in the step computation to balance optimality and feasibility. In addition, we incorporate a normalization mechanism in the design of the trust-region radius, together with Polyak momentum for gradient estimation, ensuring stable updates without gradient clipping. When the trust-region radius and the momentum parameter decay at appropriate rates, we establish global almost-sure convergence of the method. To the best of our knowledge, this is the first asymptotic convergence result for constrained stochastic optimization under heavy-tailed noise. We demonstrate the promising performance of the proposed method through extensive numerical experiments, including comparisons among its variants and with existing constrained stochastic optimization methods.
Comments32 pages, 5 figures, 3 tables
