A Parallel SGD method with Strong Convergence

Abstract This paper proposes a novel parallel stochastic gradient descent (SGD) method that is obtained by applying parallel sets of SGD iterations (each set operating on one node using the data residing in it) for finding the direction in each iteration of a batch descent method. The method has strong convergence properties. Experiments on datasets with high dimensional feature spaces show the value of this method. Introduction. We are interested in the large scale learning of linear classifiers. Let {x i , y i } be the training set associated with a binary classification problem (y i ∈ {1, −1}). Consider a linear classification model, y = sgn(w T x). Let l(w · x i , y i ) be a continuously differentiable, non-negative, convex loss function that has Lipschitz continuous gradient. This allows us to consider loss functions such as least squares, logistic loss and squared hinge loss. Hinge loss is not covered by our theory since it is non-differentiable. Our aim is to to minimize the regularized risk functional f (w)

Communication Efficient Distributed Optimization using an Approximate Newton-type Method

We present a novel Newton-type method for distributed optimization, which is particularly well suited for stochastic optimization and learning problems. For quadratic objectives, the method enjoys a linear rate of convergence which provably \emph{improves} with the data size, requiring an essentially constant number of iterations under reasonable assumptions. We provide theoretical and empirical evidence of the advantages of our method compared to other approaches, such as one-shot parameter averaging and ADMM

GIANT: Globally Improved Approximate Newton Method for Distributed Optimization

For distributed computing environment, we consider the empirical risk minimization problem and propose a distributed and communication-efficient Newton-type optimization method. At every iteration, each worker locally finds an Approximate NewTon (ANT) direction, which is sent to the main driver. The main driver, then, averages all the ANT directions received from workers to form a {\it Globally Improved ANT} (GIANT) direction. GIANT is highly communication efficient and naturally exploits the trade-offs between local computations and global communications in that more local computations result in fewer overall rounds of communications. Theoretically, we show that GIANT enjoys an improved convergence rate as compared with first-order methods and existing distributed Newton-type methods. Further, and in sharp contrast with many existing distributed Newton-type methods, as well as popular first-order methods, a highly advantageous practical feature of GIANT is that it only involves one tuning parameter. We conduct large-scale experiments on a computer cluster and, empirically, demonstrate the superior performance of GIANT.Comment: Fixed some typos. Improved writin

A parallel sgd method with strong convergence

Abstract This paper proposes a novel parallel stochastic gradient descent (SGD) method that is obtained by applying parallel sets of SGD iterations (each set operating on one node using the data residing in it) for finding the direction in each iteration of a batch descent method. The method has strong convergence properties. Experiments on datasets with high dimensional feature spaces show the value of this method. Introduction. We are interested in the large scale learning of linear classifiers. Let {x i , y i } be the training set associated with a binary classification problem (y i ∈ {1, −1}). Consider a linear classification model, y = sgn(w T x). Let l(w · x i , y i ) be a continuously differentiable, non-negative, convex loss function that has Lipschitz continuous gradient. This allows us to consider loss functions such as least squares, logistic loss and squared hinge loss. Hinge loss is not covered by our theory since it is non-differentiable. Our aim is to to minimize the regularized risk functional f (w)