Collaborative Intelligent Reflecting Surface Networks with Multi-Agent Reinforcement Learning

Intelligent reflecting surface (IRS) is envisioned to be widely applied in future wireless networks. In this paper, we investigate a multi-user communication system assisted by cooperative IRS devices with the capability of energy harvesting. Aiming to maximize the long-term average achievable system rate, an optimization problem is formulated by jointly designing the transmit beamforming at the base station (BS) and discrete phase shift beamforming at the IRSs, with the constraints on transmit power, user data rate requirement and IRS energy buffer size. Considering time-varying channels and stochastic arrivals of energy harvested by the IRSs, we first formulate the problem as a Markov decision process (MDP) and then develop a novel multi-agent Q-mix (MAQ) framework with two layers to decouple the optimization parameters. The higher layer is for optimizing phase shift resolutions, and the lower one is for phase shift beamforming and power allocation. Since the phase shift optimization is an integer programming problem with a large-scale action space, we improve MAQ by incorporating the Wolpertinger method, namely, MAQ-WP algorithm to achieve a sub-optimality with reduced dimensions of action space. In addition, as MAQ-WP is still of high complexity to achieve good performance, we propose a policy gradient-based MAQ algorithm, namely, MAQ-PG, by mapping the discrete phase shift actions into a continuous space at the cost of a slight performance loss. Simulation results demonstrate that the proposed MAQ-WP and MAQ-PG algorithms can converge faster and achieve data rate improvements of 10.7% and 8.8% over the conventional multi-agent DDPG, respectively.