Projected Semi-Stochastic Gradient Descent Method with Mini-Batch Scheme under Weak Strong Convexity Assumption
This work addresses optimization efficiency for machine learning practitioners by offering a method with better theoretical complexity and practical performance, though it appears incremental as it builds on existing variance-reduction techniques.
The paper tackles the problem of improving stochastic gradient descent (SGD) by proposing a projected semi-stochastic gradient descent method with mini-batch, achieving linear convergence under a weak strong convexity assumption without requiring strong convexity for smooth convex functions over compact polyhedral sets, which is common in machine learning.
We propose a projected semi-stochastic gradient descent method with mini-batch for improving both the theoretical complexity and practical performance of the general stochastic gradient descent method (SGD). We are able to prove linear convergence under weak strong convexity assumption. This requires no strong convexity assumption for minimizing the sum of smooth convex functions subject to a compact polyhedral set, which remains popular across machine learning community. Our PS2GD preserves the low-cost per iteration and high optimization accuracy via stochastic gradient variance-reduced technique, and admits a simple parallel implementation with mini-batches. Moreover, PS2GD is also applicable to dual problem of SVM with hinge loss.