Nesterov Accelerated Shuffling Gradient Method for Convex Optimization
This work addresses optimization efficiency for machine learning and data science applications, representing an incremental improvement over existing shuffling gradient methods.
The paper tackles convex finite-sum minimization problems by proposing NASG, which integrates Nesterov's acceleration momentum with shuffling sampling schemes, achieving an improved convergence rate of O(1/T) that outperforms other shuffling gradient methods in the convex regime.
In this paper, we propose Nesterov Accelerated Shuffling Gradient (NASG), a new algorithm for the convex finite-sum minimization problems. Our method integrates the traditional Nesterov's acceleration momentum with different shuffling sampling schemes. We show that our algorithm has an improved rate of $\mathcal{O}(1/T)$ using unified shuffling schemes, where $T$ is the number of epochs. This rate is better than that of any other shuffling gradient methods in convex regime. Our convergence analysis does not require an assumption on bounded domain or a bounded gradient condition. For randomized shuffling schemes, we improve the convergence bound further. When employing some initial condition, we show that our method converges faster near the small neighborhood of the solution. Numerical simulations demonstrate the efficiency of our algorithm.