Task-Based Information Compression for Multi-Agent Communication Problems with Channel Rate Constraints

A collaborative task is assigned to a multiagent system (MAS) in which agents are allowed to communicate. The MAS runs over an underlying Markov decision process and its task is to maximize the averaged sum of discounted one-stage rewards. Although knowing the global state of the environment is necessary for the optimal action selection of the MAS, agents are limited to individual observations. Inter-agent communication can tackle the issue of local observability, however, the limited rate of inter-agent communication prevents the agents from acquiring the precise global state information. To overcome this challenge, agents need to communicate an abstract version of their observations to each other such that the MAS compromises the minimum possible sum of rewards. We show that this problem is equivalent to a form of rate-distortion problem, which we call task-based information compression (TBIC). We introduce state aggregation for information compression (SAIC) to solve the TBIC problem. SAIC is shown to achieve near-optimal performance in terms of the achieved sum of discounted rewards. The proposed algorithm is applied to a rendezvous problem and its performance is compared with several benchmarks. Numerical experiments confirm the superiority of the proposed algorithm.