CoFi-PGMA: Counterfactual Policy Gradients under Filtered Feedback for Multi-Agent LLMs

• URL: http://arxiv.org/abs/2604.22785v1
• Date: Fri, 03 Apr 2026 22:55:23 GMT
• Title: CoFi-PGMA: Counterfactual Policy Gradients under Filtered Feedback for Multi-Agent LLMs
• Abstract summary: We introduce CoFi-PGMA, a unified framework for learning under filtered feedback in multi-agent LLM systems.<n>Our approach derives a counterfactual per-agent training objective based on marginal contribution, which corrects the learning signal under both routing and collaborative mechanisms.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Large language model (LLM) deployments increasingly rely on multi-agent architectures in which multiple models either compete through routing mechanisms or collaborate to produce a final answer. In both settings, the learning signal received by each agent is filtered by the system mechanism. Routing produces selection-gated feedback where only the chosen response is evaluated, while collaboration produces shared rewards that obscure the individual contribution of each agent. As a result, standard RLHF objectives designed for a single deployed policy become misspecified. We introduce CoFi-PGMA (Counterfactual Policy Gradients under Filtered Feedback for Multi-Agent LLMs), a unified framework for learning under filtered feedback in multi-agent LLM systems. Our approach derives a counterfactual per-agent training objective based on marginal contribution, which corrects the learning signal under both routing and collaborative mechanisms. For routing systems, the objective corresponds to off-policy corrections for selection-gated feedback, while for collaborative systems it reduces to leave-one-out difference rewards for credit assignment. We further analyze how softmax routing induces risk-sensitive incentives and provide practical training algorithms that integrate counterfactual estimators, multiturn-aware rewards, and policy optimization methods, and demonstrate the approach on a real-world reasoning dataset.

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