Modern large-scale machine learning applications require stochastic optimization algorithms to be implemented on distributed computational architectures. A key bottleneck is the communication overhead for exchanging information such as stochastic gradients among different workers. In this paper, to reduce the communication cost, we propose a convex optimization formulation to minimize the coding length of stochastic gradients. The key idea is to randomly drop out coordinates of the stochastic gradient vectors and amplify the remaining coordinates appropriately to ensure the sparsified gradient to be unbiased. To solve the optimal sparsification efficiently, a simple and fast algorithm is proposed for an approximate solution, with a theoretical guarantee for sparseness.

Neural Information Processing Systems http://nips.cc/

We study the stochastic optimization of canonical correlation analysis (CCA), whose objective is nonconvex and does not decouple over training samples. Although several stochastic gradient based optimization algorithms have been recently proposed to solve this problem, no global convergence guarantee was provided by any of them. Inspired by the alternating least squares/power iterations formulation of CCA, and the shift-and-invert preconditioning method for PCA, we propose two globally convergent meta-algorithms for CCA, both of which transform the original problem into sequences of least squares problems that need only be solved approximately. We instantiate the meta-algorithms with state-of-the-art SGD methods and obtain time complexities that significantly improve upon that of previous work. Experimental results demonstrate their superior performance.

We consider Bayesian methods for multi-information source optimization (MISO), in which we seek to optimize an expensive-to-evaluate black-box objective function while also accessing cheaper but biased and noisy approximations ("information sources"). We present a novel algorithm that outperforms the state of the art for this problem by using a Gaussian process covariance kernel better suited to MISO than those used by previous approaches, and an acquisition function based on a one-step optimality analysis supported by efficient parallelization. We also provide a novel technique to guarantee the asymptotic quality of the solution provided by this algorithm. Experimental evaluations demonstrate that this algorithm consistently finds designs of higher value at less cost than previous approaches.

We suggest a general oracle-based framework that captures different parallel stochastic optimization settings described by a dependency graph, and derive generic lower bounds in terms of this graph. We then use the framework and derive lower bounds for several specific parallel optimization settings, including delayed updates and parallel processing with intermittent communication. We highlight gaps between lower and upper bounds on the oracle complexity, and cases where the "natural" algorithms are not known to be optimal.

Modern large-scale machine learning applications require stochastic optimization algorithms to be implemented on distributed computational architectures. A key bottleneck is the communication overhead for exchanging information such as stochastic gradients among different workers. In this paper, to reduce the communication cost, we propose a convex optimization formulation to minimize the coding length of stochastic gradients. The key idea is to randomly drop out coordinates of the stochastic gradient vectors and amplify the remaining coordinates appropriately to ensure the sparsified gradient to be unbiased. To solve the optimal sparsification efficiently, a simple and fast algorithm is proposed for an approximate solution, with a theoretical guarantee for sparseness.

Neural Information Processing Systems http://nips.cc/