Title: Stochastic Difference-of-Convex Optimization with Momentum Show Chinese title

Title: 带有动量的随机凸差优化

Abstract: Stochastic difference-of-convex (DC) optimization is prevalent in numerous machine learning applications, yet its convergence properties under small batch sizes remain poorly understood. Existing methods typically require large batches or strong noise assumptions, which limit their practical use. In this work, we show that momentum enables convergence under standard smoothness and bounded variance assumptions (of the concave part) for any batch size. We prove that without momentum, convergence may fail regardless of stepsize, highlighting its necessity. Our momentum-based algorithm achieves provable convergence and demonstrates strong empirical performance. Show Chinese abstract

Abstract: 随机凸差（DC）优化在许多机器学习应用中很常见，但其在小批量尺寸下的收敛性特性仍然不明确。 现有方法通常需要大批次或强噪声假设，这限制了它们的实际应用。 在本工作中，我们表明动量能够在标准光滑性和有界方差假设（凹部分）下，对于任何批次大小都能实现收敛。 我们证明了没有动量的情况下，无论步长如何，收敛都可能失败，突显了动量的必要性。 我们的基于动量的算法实现了可证明的收敛性，并表现出强大的经验性能。