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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.22785 |
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| _version_ | 1866910163649167360 |
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| author | Tong, Stela Ben-Gal, Elai |
| author_facet | Tong, Stela Ben-Gal, Elai |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22785 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | CoFi-PGMA: Counterfactual Policy Gradients under Filtered Feedback for Multi-Agent LLMs Tong, Stela Ben-Gal, Elai Machine Learning 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. |
| title | CoFi-PGMA: Counterfactual Policy Gradients under Filtered Feedback for Multi-Agent LLMs |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2604.22785 |