How can I ensure my LLM agents converge to optimal solutions in a human-robot system?
Human Machine Co-Adaptation Model and Its Convergence Analysis
This paper proposes a Cooperative Adaptive Markov Decision Process (CAMDP) model for robot-assisted rehabilitation, where a patient (Agent0) and a robot (Agent1) learn to cooperate. It focuses on establishing conditions for the convergence of the learning process to a stable, ideally optimal, joint policy (Nash Equilibrium). The key contribution for LLM-based multi-agent systems is the theoretical analysis of convergence and uniqueness of solutions in a cooperative multi-agent setting, which is relevant for ensuring predictable and reliable behavior in such systems. The paper explores different policy update rules (simultaneous vs. alternating) and proposes methods like less greedy policy improvement and model simplification (policy pruning, state reduction) to mitigate challenges like convergence to local optima and frequent policy switching, especially relevant to LLM agents collaborating on complex tasks.