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Decentralized Local Stochastic Extra-Gradient for Variational Inequalities
Aleksandr Beznosikov · Pavel Dvurechenskii · Anastasiia Koloskova · Valentin Samokhin · Sebastian Stich · Alexander Gasnikov

Tue Dec 06 09:00 AM -- 11:00 AM (PST) @

We consider distributed stochastic variational inequalities (VIs) on unbounded domains with the problem data that is heterogeneous (non-IID) and distributed across many devices. We make a very general assumption on the computational network that, in particular, covers the settings of fully decentralized calculations with time-varying networks and centralized topologies commonly used in Federated Learning. Moreover, multiple local updates on the workers can be made for reducing the communication frequency between the workers.We extend the stochastic extragradient method to this very general setting and theoretically analyze its convergence rate in the strongly-monotone, monotone, and non-monotone (when a Minty solution exists) settings. The provided rates explicitly exhibit the dependence on network characteristics (e.g., mixing time), iteration counter, data heterogeneity, variance, number of devices, and other standard parameters. As a special case, our method and analysis apply to distributed stochastic saddle-point problems (SPP), e.g., to the training of Deep Generative Adversarial Networks (GANs) for which decentralized training has been reported to be extremely challenging. In experiments for the decentralized training of GANs we demonstrate the effectiveness of our proposed approach.

Author Information

Aleksandr Beznosikov (Moscow Institute of Physics and Technology)
Pavel Dvurechenskii (Weierstrass Institute, Berlin)

Since 2015 Research assistant, Research Group 6 "Stochastic Algorithms and Nonparametric Statistics", Weierstrass Institute for Applied Analysis and Stochastics, Berlin 2014 - 2015 Research assistant, Institute for Information Transmission Problems, Moscow, Russia 2009 - 2015 Junior researcher, Moscow Institute of Physics and Technology, Moscow, Russia 2013 Ph.D., Moscow Institute of Physics and Technology, Moscow, Russia 2010 Master's Diploma, Moscow Institute of Physics and Technology, Moscow, Russia 2008 Bachelor's Diploma, Moscow Institute of Physics and Technology, Moscow, Russia

Anastasiia Koloskova (EPFL)
Valentin Samokhin (Skolkovo Institute of Science and Technology)
Sebastian Stich (CISPA)
Alexander Gasnikov (Moscow Institute of Physics and Technology)

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