Variance-Reduced Conditional Gradient Methods under Markovian Sampling for Nonconvex Composite Optimization

What the math gives to ML

The paper develops a projection-free stochastic optimization method that remains controlled when gradients come from one dependent Markov trajectory rather than independent minibatches. Its transferable asset is the coupling of consecutive multilevel averages: fine-minus-coarse gradient corrections can have variance tied to parameter movement instead of raw gradient noise, while clipping enforces bounded updates. A practical adaptation is a Markov-aware variance-reduced gradient estimator inside online neural-network training, especially for reinforcement learning, time-series prediction, MCMC-generated data, and streaming sensors where shuffling is impossible. The main empirical question is whether this reduces gradient autocorrelation and improves validation loss per consumed stream sample without harming performance on iid data.