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The stochastic compositional minimax problem has attracted a surge ofattention in recent years since it covers many emerging machine learningmodels. Meanwhile, due to the emergence of distributed data, optimizing thiskind of problem under the decentralized setting becomes badly needed. However,the compositional structure in the loss function brings unique challenges todesigning efficient decentralized optimization algorithms. In particular, ourstudy shows that the standard gossip communication strategy cannot achievelinear speedup for decentralized compositional minimax problems due to thelarge consensus error about the inner-level function. To address this issue, wedeveloped a novel decentralized stochastic compositional gradient descentascent with momentum algorithm to reduce the consensus error in the inner-levelfunction. As such, our theoretical results demonstrate that it is able toachieve linear speedup with respect to the number of workers. We believe thisnovel algorithmic design could benefit the development of decentralizedcompositional optimization. Finally, we applied our methods to the imbalancedclassification problem. The extensive experimental results provide evidence forthe effectiveness of our algorithm.

Achieving Linear Speedup in Decentralized Stochastic Compositional Minimax Optimization