arXiv Machine Learning By El Mahdi Chayti, Mohamad Fakhouri

Stochastic Compositional Optimization via Hybrid Momentum Frank--Wolfe

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arXiv:2605. 15350v2 Announce Type: replace-cross Abstract: Stochastic compositional optimization minimizes $F(f(x), x)$ over a compact convex set when the inner map $f$ is available only through noisy samples.

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arXiv Machine Learning
Oct 3

Optimal Momentum Methods for Stochastic Multilevel Compositional Optimization

The paper studies stochastic multi‑level optimization where the objective is a nested composition of smooth non‑convex functions. It introduces momentum‑based estimators that track function values at each level, achieving an optimal sample complexity of ≠(ε⁻⁴) for finding an ε‑stationary point without relying on average smoothness assumptions. The authors also present a batch‑free variant using first‑order approximations and clipping, and demonstrate the methods on risk‑averse portfolio optimization and hierarchical tilted empirical risk minimization.

By Wei Jiang, Rui Yan, Sifan Yang, Yuanyu Wan, Lijun Zhang, Zechao Li