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However, most MARL fine-tuning approaches rely on predefined execution protocols, which often require centralized execution. Decentralized LLM collaboration is more appealing in practice, as agents can run inference in parallel with flexible deployments. Also, current approaches use Monte Carlo methods for fine-tuning, which suffer from high variance and thus require more samples to train effectively. Actor-critic methods are prevalent in MARL for dealing with these issues; thus, we developed Multi-Agent Actor-Critic (MAAC) methods to optimize decentralized LLM collaboration. In this paper, we analyze when and why these MAAC methods are beneficial. We propose 2 MAAC approaches, \\textbf{CoLLM-CC} with a \\textbf{C}entralized \\textbf{C}ritic and \\textbf{CoLLM-DC} with \\textbf{D}ecentralized \\textbf{C}ritics. 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