The stochastic compositional minimax problem has attracted a surge of
attention in recent years since it covers many emerging machine learning
models. Meanwhile, due to the emergence of distributed data, optimizing this
kind of problem under the decentralized setting becomes badly needed. However,
the compositional structure in the loss function brings unique challenges to
designing efficient decentralized optimization algorithms. In particular, our
study shows that the standard gossip communication strategy cannot achieve
linear speedup for decentralized compositional minimax problems due to the
large consensus error about the inner-level function. To address this issue, we
developed a novel decentralized stochastic compositional gradient descent
ascent with momentum algorithm to reduce the consensus error in the inner-level
function. As such, our theoretical results demonstrate that it is able to
achieve linear speedup with respect to the number of workers. We believe this
novel algorithmic design could benefit the development of decentralized
compositional optimization. Finally, we applied our methods to the imbalanced
classification problem. The extensive experimental results provide evidence for
the effectiveness of our algorithm.

通过开发一种新的具有动量的分布式随机组合梯度下降上升算法，我们解决了分布式组合极小化问题中内层函数的共识误差，并证明了其能够实现线性加速。我们相信这种算法设计能够促进分布式组合优化的发展。对于不平衡分类问题，我们的广泛实验结果证明了算法的有效性。