Multi-Agent Reinforcement Learning in Non-Cooperative Stochastic Games Using Large Language Models

We study the use of large language models (LLMs) to integrate high-level knowledge in stochastic games using reinforcement learning with reward machines to encode non-Markovian and Markovian reward functions. In non-cooperative games, one challenge is to provide agents with knowledge about the task efficiently to speed up the convergence to an optimal policy. We aim to provide this knowledge in the form of deterministic finite automata (DFA) generated by LLMs (LLM-generated DFA). Additionally, we use reward machines (RMs) to encode the temporal structure of the game and the non-Markovian or Markovian reward functions. Our proposed algorithm, LLM-generated DFA for Multi-agent Reinforcement Learning with Reward Machines for Stochastic Games (StochQ-RM), can learn an equivalent reward machine to the ground truth reward machine (specified task) in the environment using the LLM-generated DFA. Additionally, we propose DFA-based q-learning with reward machines (DBQRM) to find the best responses for each agent using Nash equilibrium in stochastic games. Despite the fact that the LLMs are known to hallucinate, we show that our method is robust and guaranteed to converge to an optimal policy. Furthermore, we study the performance of our proposed method in three case studies.