Multiagent Evolution Strategy With Cooperative and Cumulative Step Adaptation for Black-Box Distributed Optimization

In recent years, black-box distributed optimization (DBO) has been widely studied to solve complex optimization problems in multiagent systems (MASs), such as hyperparameter optimization of distributed machine learning. However, most existing methods use a fixed or diminishing step size to sample and search in the black box optimization space, which makes it challenging to maintain optimization efficiency on different optimization problems. In this work, we propose a multiagent evolution strategy with cooperative and cumulative step adaptation (CCSA-DES). In CCSA-DES, each agent executes the algorithm to sample and explores its local objective function, and communicates with other agents to optimize the global objective function cooperatively, which is the sum of local objective functions. To improve the sampling adaptability, we design a cooperative and cumulative step adaptation method (CCSA) consisting of inner adaptation and outer adaptation. By detecting the evolution path of the MAS, CCSA decreases the step size when the evolution directions of agents are conflicting and increases the step size when consistent. In terms of theoretical analysis, we first discuss the working principle of CCSA, and then discuss the system consensus of CCSA-DES. In terms of experimental verification, CCSA-DES achieves better-consensus performance and competitive solution quality compared with state-of-the-art algorithms for DBO.