Doubly Accelerated Stochastic Variance Reduced Dual Averaging Method for Regularized Empirical Risk Minimization
This work addresses the need for faster and more efficient optimization in machine learning, particularly for large-scale datasets, by enhancing mini-batch processing, though it appears incremental as it builds on existing accelerated stochastic methods.
The paper tackles the problem of efficiently solving convex regularized empirical risk minimization in mini-batch settings by developing a new accelerated stochastic gradient method that incorporates a 'double acceleration' technique and variance reduction. The result shows that the method improves mini-batch efficiencies, requiring only size √n mini-batches to achieve optimal iteration complexities for both non-strongly and strongly convex objectives, and achieves the best known convergence rates even in non-mini-batch settings.
In this paper, we develop a new accelerated stochastic gradient method for efficiently solving the convex regularized empirical risk minimization problem in mini-batch settings. The use of mini-batches is becoming a golden standard in the machine learning community, because mini-batch settings stabilize the gradient estimate and can easily make good use of parallel computing. The core of our proposed method is the incorporation of our new "double acceleration" technique and variance reduction technique. We theoretically analyze our proposed method and show that our method much improves the mini-batch efficiencies of previous accelerated stochastic methods, and essentially only needs size $\sqrt{n}$ mini-batches for achieving the optimal iteration complexities for both non-strongly and strongly convex objectives, where $n$ is the training set size. Further, we show that even in non-mini-batch settings, our method achieves the best known convergence rate for both non-strongly and strongly convex objectives.