#### Shuffling Gradient-Based Methods with Momentum

##### Trang H. Tran, Lam M. Nguyen, Quoc Tran-Dinh

We combine two advanced ideas widely used in optimization for machine learning: shuffling strategy and momentum technique to develop a novel shuffling gradient-based method with momentum to approximate a stationary point of non-convex finite-sum minimization problems. While our method is inspired by momentum techniques, its update is significantly different from existing momentum-based methods. We establish that our algorithm achieves a state-of-the-art convergence rate for both constant and diminishing learning rates under standard assumptions (i.e., $L$-smoothness and bounded variance). When the shuffling strategy is fixed, we develop another new algorithm that is similar to existing momentum methods. This algorithm covers the single-shuffling and incremental gradient schemes as special cases. We prove the same convergence rate of this algorithm under the $L$-smoothness and bounded gradient assumptions. We demonstrate our algorithms via numerical simulations on standard datasets and compare them with existing shuffling methods. Our tests have shown encouraging performance of the new algorithms.

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