从离线数据中学习自私智能体的重叠联盟,实现近似纳什稳定。
Offline Learning of Nash Stable Coalition Structures with Possibly Overlapping Coalitions
- 基于历史交互数据推断智能体偏好,支持重叠联盟。
- 在两种反馈下均能恢复近似纳什稳定联盟结构。
- 算法样本复杂度低,适合数据稀缺场景。
联盟形成关注自私智能体根据自身偏好进行战略协作。传统模型常假设联盟互不重叠且偏好完全已知,这在实际中未必成立。本文提出一种新模型,允许智能体同时参与多个联盟,且初始偏好未知。仅通过存储过去交互及对应效用反馈的固定离线数据集,目标是从中高效推断偏好。研究了两类效用反馈:个体级与联盟级。对两类模型,识别出数据集信息充足时可实现近似纳什稳定联盟划分的条件,即任一智能体无法通过单方面偏离提升自身效用。此外,追求低样本复杂度,仅需小数据集即可获得理想近似。在个体级反馈下,给出一个样本高效的算法,在信息覆盖充分必要条件下可获近似纳什稳定划分。而在联盟级反馈下,需更强假设才可实现高效学习。实验表明,算法在多种设置下均快速收敛至低近似水平的纳什稳定性。
原文摘要 · Abstract (English)
Coalition formation concerns strategic collaborations of selfish agents that form coalitions based on their preferences. It is often assumed that coalitions are disjoint and preferences are fully known, which may not hold in practice. In this paper, we thus present a new model of coalition formation with possibly overlapping coalitions under partial information, where selfish agents may be part of multiple coalitions simultaneously and their full preferences are initially unknown. Instead, information about past interactions and associated utility feedback is stored in a fixed offline dataset, and we aim to efficiently infer the agents' preferences from this dataset. We analyze the impact of diverse dataset information constraints by studying two types of utility feedback that can be stored in the dataset: agent- and coalition-level utility feedback. For both feedback models, we identify assumptions under which the dataset covers sufficient information for an offline learning algorithm to infer preferences and use them to recover a partition that is (approximately) Nash stable, in which no agent can improve her utility by unilaterally deviating. Our additional goal is devising algorithms with low sample complexity, requiring only a small dataset to obtain a desired approximation to Nash stability. Under agent-level feedback, we provide a sample-efficient algorithm proven to obtain an approximately Nash stable partition under a sufficient and necessary assumption on the information covered by the dataset. However, under coalition-level feedback, we show that only under a stricter assumption is sufficient for sample-efficient learning. Still, in multiple cases, our algorithms' sample complexity bounds have optimality guarantees up to logarithmic factors. Finally, extensive experiments show that our algorithm converges to a low approximation level to Nash stability across diverse settings.
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