Large-scale learning with AdaGrad on Spark

Stochastic Gradient Descent (SGD) is a simple yet very efficient online learning algorithm for optimizing convex (and often non-convex) functions and one of the most popular stochastic optimization methods in machine learning today. One drawback of SGD is that it is sensitive to the learning rate hyper-parameter. The Adaptive Sub-gradient Descent, AdaGrad, dynamically incorporates knowledge of the geometry of the data observed in earlier iterations to calculate a different learning rate for every feature. In this work, we implement a distributed version of AdaGrad for large-scale machine learning tasks using Apache Spark. Apache Spark is a fast cluster computing engine that provides similar scalability and fault tolerance properties to MapReduce, but in contrast to Hadoop´s two-stage disk-based MapReduce paradigm, Spark´s multi-stage in-memory primitives allow user programs to load data into a cluster´s memory and query it repeatedly, which makes it ideal for building scalable machine learning applications. We empirically evaluate our implementation on large-scale real-world problems in the machine learning canonical tasks of classification and regression. Comparing our implementation of AdaGrad with the SGD scheduler currently available in Spark´s Machine Learning Library (MLlib), we experimentally show that AdaGrad saves time by avoiding manually setting a learning-rate hyperparameter, converges fast and can even achieve better generalization errors.