Stochastic Compositional Optimization via Hybrid Momentum Frank--Wolfe
Stochastic compositional optimization minimizes $F(f(x), x)$ over a compact convex set when the inner map $f$ is available only through noisy samples. We propose Hybrid Momentum Stochastic Frank--Wolfe, a projection-free method for outer functions $F$ that are jointly convex and Lipschitz but not necessarily differentiable, such as maxima, CVaR, and norms. The method tracks the Jacobian and the value of $f$ with momentum, using a Taylor correction for the value, and passes the tracked linearization to a generalized linear minimization oracle. Under finite-variance noise, it attains an expected generalized Frank--Wolfe gap of order $K^{-1/4}$ for non-convex objectives and, when the lineari...
| Authors | El Mahdi Chayti, Mohamad Fakhouri |
|---|---|
| Primary category | math.OC |
| Published | 14 May 2026 |
| Last updated at source | 9 October 2026 |
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