Social deduction games (SDGs) require agents to reason under partial observability by maintaining relational beliefs about hidden roles, team alignments, suspicion, and others’ perceptions. While recent LLM-agent approaches improve gameplay through prompting, reflection, and preference optimization, they often optimize actions and in-game speech without explicitly grounding them in such beliefs. This frequently leads to strategically inconsistent behavior, especially for compact LLM agents. We introduce Multi-Agent Relational Belief Optimization (MARBO), a belief-grounded preference optimization framework that leverages relational beliefs to guide strategic decisions and in-game speech. MARBO selectively provides preference feedback only when behaviors are supported by reliable relational beliefs and lead to strategically favorable social outcomes, encouraging more consistent learning under uncertainty. Experiments on representative SDGs, including Werewolf and Among Us, show that MARBO enables compact LLM agents to consistently outperform existing baselines.

Mathematical question answering over long-form documents is challenging across domains like finance or Wikipedia due to the abundance of candidate arguments within evidence, which complicates recognizing proper arguments for mathematical reasoning and poses hard to learning. In this paper, we propose an approach for training a generator to improve argument recognition. Our method enhances the probabilities of proper arguments in a reasoning program generation so that the arguments comprising the ground truth have higher weights. The proposed approach consists of an argument aggregator to model the probabilities in each candidate generation and an argument set loss to compute the cross-entropy between that probability and the candidates’ existence in the ground truth in terms of the argument set. In our experiments, we show performance improvements of 3.62% and 3.98% in execution accuracy and program accuracy, respectively, over the existing FinQANet model based on a financial mathematical QA dataset. Also, we observed that the similarity of argument sets between the generated program and the ground truth improved by about 2.9%, indicating a mitigation of the misrecognition problem.