arXiv cs.AI· Ahmed Mahrous, Roberto Di Pietro·· 13 小时前AI 评分31
多智能体表演性预测的反射性阈值：NeurIPS 2026 论文提出谱阈值相变
The Reflexivity Threshold: A Phase Transition for Multi-Agent Performative Prediction
AI 导读
研究多智能体表演性预测中的重复重训练，提出反射性矩阵 Γ，其谱半径越过 1 即为稳定学习与最坏情况学习受阻之间的阈值。阈值以下重复重训练几何收敛到唯一表演性稳定均衡，累积超额损失在时间跨度上一致有界；阈值以上构造的噪声超临界实例中，每个局部信息学习者的期望累积超额损失线性增长，跨度可达 1/(ρ(Γ)-1) 量级。该结果以上下界刻画阈值行为，并将此前单智能体标量阈值作为特例纳入。
正文 · 原文
Abstract:Many learning systems are performative: once deployed, their predictions change the data distribution on which future models are trained. In multi-agent settings, this feedback is routed through a network of interacting learners, so stability depends not only on the strength of performativity but also on who affects whom. We study repeated retraining in multi-agent performative prediction and identify a spectral threshold that separates stable learning from worst-case learning obstruction. Prior work often collapses cross-agent feedback into a scalar contraction constant, missing this network structure. We instead introduce the reflexivity matrix $\Gamma$, which records how strongly one agent's deployment can move another agent's best response, defined from per-agent gradient sensitivities and curvature parameters. The threshold occurs when the spectral radius of this matrix crosses one. Below the threshold, repeated retraining converges geometrically to a unique performatively stable equilibrium, with cumulative excess loss bounded uniformly in the time horizon. Above the threshold, we construct noisy supercritical instances in which every local-information learner incurs expected cumulative excess loss growing linearly for horizons up to order $1/(\rho(\Gamma)-1)$. Together, these results characterize the threshold behavior through upper and lower bounds and recover the single-agent scalar threshold from prior work as a special case.
| Comments: | Accepted at NeurIPS 2026. 20 pages, including appendix and checklist. Code: this https URL |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2610.29577 [cs.LG] |
| (or arXiv:2610.29577v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.29577 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Ahmed Mahrous [view email]
[v1]
Wed, 21 Oct 2026 11:20:29 UTC (84 KB)
来源：arXiv cs.AI · arxiv.org