Modern large-scale ML 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 authors 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, as well as lower bounds for several specific parallel optimization settings. They highlight gaps between lower and upper bounds on the oracle complexity, and cases where the “natural” algorithms are not known to be optimal.
Sparse Principal Component Analysis (SPCA) and Sparse Linear Regression (SLR) have a wide range of applications and have attracted attention as canonical examples of statistical problems in high dimension. A variety of algorithms have been proposed for both SPCA and SLR, but an explicit connection between the two had not been made. This paper shows how to efficiently transform a black-box solver for SLR into an algorithm for SPCA.