An Efficient Stochastic Algorithm for Decentralized Nonconvex-Strongly-Concave Minimax Optimization
This addresses optimization problems in distributed systems, offering incremental improvements in efficiency for multi-agent networks.
The paper tackles decentralized nonconvex-strongly-concave minimax optimization in multi-agent networks by proposing the DREAM algorithm, which achieves the best-known theoretical guarantee with $\mathcal{O}(\min (κ^3ε^{-3},κ^2 \sqrt{N} ε^{-2} ))$ SFO calls and $ ilde{\mathcal{O}}(κ^2 ε^{-2})$ communication rounds for finding ε-stationary points.
This paper studies the stochastic nonconvex-strongly-concave minimax optimization over a multi-agent network. We propose an efficient algorithm, called Decentralized Recursive gradient descEnt Ascent Method (DREAM), which achieves the best-known theoretical guarantee for finding the $ε$-stationary points. Concretely, it requires $\mathcal{O}(\min (κ^3ε^{-3},κ^2 \sqrt{N} ε^{-2} ))$ stochastic first-order oracle (SFO) calls and $\tilde{\mathcal{O}}(κ^2 ε^{-2})$ communication rounds, where $κ$ is the condition number and $N$ is the total number of individual functions. Our numerical experiments also validate the superiority of DREAM over previous methods.