Joint caching and transmission optimization problem is challenging due to the deep coupling between decisions. This paper proposes an iterative distributed multi-agent learning approach to jointly optimize caching and transmission. The goal of this approach is to minimize the total transmission delay of all users. In this iterative approach, each iteration includes caching optimization and transmission optimization. A multi-agent reinforcement learning (MARL)-based caching network is developed to cache popular tasks, such as answering which files to evict from the cache and which files to storage. Based on the cached files of the caching network, the transmission network transmits cached files for users by single transmission (ST) or joint transmission (JT) with multi-agent Bayesian learning automaton (MABLA) method. And then users access the edge servers with the minimum transmission delay. The experimental results demonstrate the performance of the proposed multi-agent learning approach.