In this work, we consider a connected network of finitely many agents working cooperatively to solve a min-max problem with convex-concave structure. We propose a decentralised first-order algorithm which can be viewed as a non-trivial combination of two algorithms: PG-EXTRA for decentralised minimisation problems and the forward reflected backward method for (non-distributed) min-max problems. In each iteration of our algorithm, each agent computes the gradient of the smooth component of its local objective function as well as the proximal operator of its nonsmooth component, following by a round of communication with its neighbours. Our analysis shows that the sequence generated by the method converges under standard assumptions with non-decaying stepsize.

翻译：本研究考虑由有限个智能体构成的连通网络，这些智能体通过协作求解具有凸-凹结构的极小-极大问题。我们提出一种去中心化一阶算法，该算法可视为两种方法的非平凡结合：针对去中心化最小化问题的PG-EXTRA算法，以及针对（非分布式）极小-极大问题的前向反射后向方法。在本算法的每次迭代中，每个智能体计算其局部目标函数光滑分量的梯度及其非光滑分量的邻近算子，随后与其相邻节点进行一轮通信。分析表明，在标准假设条件下，该方法生成的序列能以非递减步长收敛。