Variance-Reduced Conditional Gradient Methods under Markovian Sampling for Nonconvex Composite Optimization
We study stochastic composite nonconvex optimization over a compact convex set when gradient samples arrive along a single trajectory of a fixed ergodic Markov chain. Existing single-trajectory variance-reduction theory covers smooth unconstrained objectives; we address the projection-free composite setting using the generalized Frank-Wolfe gap. We propose MC-ALFCG, which combines a momentum conditional-gradient method with coupled capped multilevel Monte Carlo estimation and per-iteration clipping. The deepest nested average uses consecutive states from the same trajectory, yielding conditional bias $O(τ_{\mathrm{mix}}/T)$ uniformly over the starting state, while coupling controls the gr...
| Authors | Zhaojun Peng |
|---|---|
| Primary category | math.OC |
| Published | 28 July 2026 |
| Last updated at source | 28 July 2026 |
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