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This paper describes a third-generation parameter server framework for distributed machine learning. This framework offers two relaxations to balance system performance and algorithm efficiency. We propose a new algorithm that takes advantage of this framework to solve non-convex non-smooth problems with convergence guarantees. We present an in-depth analysis of two large scale machine learning problems ranging from -regularized logistic regression on CPUs to reconstruction ICA on GPUs, using 636TB of real data with hundreds of billions of samples and dimensions. We demonstrate using these examples that the parameter server framework is an effective and straightforward way to scale machine learning to larger problems and systems than have been previously achieved.