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Distributed Saddle-Point Problems: Lower Bounds, Near-Optimal and Robust Algorithms
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This paper focuses on the distributed optimization of stochastic saddle point problems. The first part of the paper is devoted to lower bounds for the centralized and decentralized distributed methods for smooth (strongly) convex-(strongly) concave saddle point problems, as well as the near-optimal algorithms by which these bounds are achieved. Next, we present a new federated algorithm for centralized distributed saddle-point problems - Extra Step Local SGD. The theoretical analysis of the new method is carried out for strongly convex-strongly concave and non-convex-non-concave problems. In the experimental part of the paper, we show the effectiveness of our method in practice. In particular, we train GANs in a distributed manner.
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Cited by 1 Pith paper
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An Optimistic Gradient Tracking Method for Distributed Minimax Optimization
DOGT and its accelerated variant ADOGT achieve optimal communication complexity O(κ log(1/ε)/√(1-√ρ_W)) for distributed strongly convex-strongly concave minimax optimization over networks.
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