The escalating complexity of modern machine learning necessitates solving challenging non-convex optimization problems, particularly in high-dimensional regimes and scenarios contaminated by gross outliers. Traditional approaches, relying on convex relaxations or specialized local search heuristics, frequently succumb to suboptimal local minima and fail to recover the true underlying discrete structures. In this paper, we propose treating these non-convex challenges as a global search problem and introduce a unified framework based on Quantum-Inspired Evolutionary Optimization (QIEO). By leveraging a probabilistic representation inspired by quantum superposition, QIEO maintains a global view of the search space, enabling it to tunnel through local optima that trap conventional gradient-based and greedy solvers. We comprehensively evaluate QIEO across diverse non-convex applications, including sparse signal recovery (gene expression analysis and compressed sensing) and robust linear regression. Extensive benchmarking against state-of-the-art continuous solvers (ADAM, Differential Evolution), classical metaheuristics (Genetic Algorithms), and specialized non-convex algorithms (Iterative Hard Thresholding) demonstrates that QIEO consistently achieves superior structural fidelity, lower mean squared error, and enhanced robustness without support inflation. Our findings suggest that embracing a quantum-inspired global search provides a resilient, unified paradigm for overcoming the inherent intractability of discrete nonconvex machine learning landscapes.

翻译：现代机器学习的日益复杂性要求解决具有挑战性的非凸优化问题，尤其是在高维场景和受粗大异常值污染的情况下。依赖于凸松弛或专用局部搜索启发式的传统方法，常陷入次优局部极小值，且无法恢复真实潜在的离散结构。本文提出将这些非凸挑战视为全局搜索问题，并引入一个基于量子启发进化优化（QIEO）的统一框架。通过利用受量子叠加启发的概率表示，QIEO能够保持对搜索空间的全局视角，从而穿透困住传统基于梯度和贪婪求解器的局部最优解。我们在多种非凸应用上全面评估了QIEO，包括稀疏信号恢复（基因表达分析与压缩感知）以及稳健线性回归。与最先进的连续求解器（ADAM、差分进化）、经典元启发式（遗传算法）以及专用非凸算法（迭代硬阈值）进行的广泛基准测试表明，QIEO在不增加支撑集膨胀的情况下，始终能实现更优的结构保真度、更低的均方误差以及更强的稳健性。我们的研究结果表明，采用量子启发的全局搜索为克服离散非凸机器学习景观内在的难解性提供了一种稳健且统一的范式。