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Frontiers in Artificial Intelligence is a series of public lectures at Microsoft Research Cambridge featur-ing leading researchers in the field, focusing on the cutting edge topics at the intersection of machine learning, statistics, and artificial intelligence. Students, scientists, and engineers in academia and in-dustry are all welcome to join us for these exciting talks and the opportunity to socialize with the Cam-bridge AI/ML community.
Optimal algorithms for smooth and strongly convex distributed optimization in networks
Francis Bach, INRIA
In this work, we determine the optimal convergence rates for strongly convex and smooth distributed optimization in two settings: centralized and decentralized communications over a network. For centralized (i.e. master/slave) algorithms, we show that distributing Nesterov’s accelerated gradient descent is optimal and achieves a precision in time that depends on the condition number of the (global) function to optimize, the diameter of the network, and the time needed to communicate values between two neighbors (resp. perform local computations). For decentralized algorithms based on gossip, we provide the first optimal algorithm, called the multi-step dual accelerated (MSDA) method, that achieves the a precision that depends on the condition number of the local functions and the (normalized) eigengap of the gossip matrix used for communication between nodes. We then verify the efficiency of MSDA against state-of-the-art methods for two problems: least-squares regression and classification by logistic regression. (joint work with Kevin Scaman, Sébastien Bubeck, Yin Tat Lee, and Laurent Massoulié)