As the complexity of deep learning (DL) networks and training data grows enormously, methods that scale with computation are becoming the future of artificial intelligence (AI) development. In this regard, the interplay between machine learning (ML) and high-performance computing (HPC) is an innovative paradigm to speed up the efficiency of AI research and development. However, building and operating an HPC/AI converged system require broad knowledge to leverage the latest computing, networking, and storage technologies. Moreover, an HPC-based AI computing environment needs an appropriate resource allocation and monitoring strategy to efficiently utilize the system resources. In this regard, we introduce a technique for building and operating a high-performance AI-computing environment with the latest technologies. Specifically, an HPC/AI converged system is configured inside Gwangju Institute of Science and Technology (GIST), called GIST AI-X computing cluster, which is built by leveraging the latest Nvidia DGX servers, high-performance storage and networking devices, and various open source tools. Therefore, it can be a good reference for building a small or middlesized HPC/AI converged system for research and educational institutes. In addition, we propose a resource allocation method for DL jobs to efficiently utilize the computing resources with multi-agent deep reinforcement learning (mDRL). Through extensive simulations and experiments, we validate that the proposed mDRL algorithm can help the HPC/AI converged cluster to achieve both system utilization and power consumption improvement. By deploying the proposed resource allocation method to the system, total job completion time is reduced by around 20% and inefficient power consumption is reduced by around 40%.