SMG: A Shuffling Gradient-Based Method with Momentum
This work provides an incremental improvement in optimization algorithms for machine learning practitioners dealing with non-convex finite-sum problems.
This paper introduces Shuffling Momentum Gradient (SMG), a new optimization method for non-convex finite-sum problems that combines shuffling strategies and momentum. It achieves state-of-the-art convergence rates for any shuffling strategy with both constant and diminishing learning rates, and numerical simulations show encouraging performance.
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, coined Shuffling Momentum Gradient (SMG), for non-convex finite-sum optimization problems. While our method is inspired by momentum techniques, its update is fundamentally different from existing momentum-based methods. We establish state-of-the-art convergence rates of SMG for any shuffling strategy using either constant or diminishing learning rate 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, and prove the same convergence rates for 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.