In many multi-agent applications, tasks yield rewards only when executed by a coalition meeting an unknown size threshold; otherwise, feedback is fully censored. This censorship creates an identifiability problem: agents cannot distinguish stochastic failure from insufficient coordination. We formalize this setting as the Threshold-Activated Cooperative Multi-Armed Bandit (TAC-MAB) and analyze it under both centralized and decentralized coordination. We show that a centralized algorithm (C-TAC) achieves cumulative regret O(log T), decomposed into a structural-search term that captures the cost of resolving feasibility under censored feedback and a statistical-monitoring term for value estimation. We then introduce D-TAC, a decentralized event-triggered protocol in which agents synchronize only when their structural beliefs change. Empirically, D-TAC achieves a 23x reduction in communication relative to the centralized baseline while preserving feasibility alignment under conservative belief fusion. These results characterize the coordination cost of learning under censored feedback and show that near-centralized communication efficiency is achievable without continuous synchronization.

翻译：在许多多智能体应用中，任务仅在满足未知规模阈值的联盟执行时才会产生奖励；否则，反馈完全被删失。这种删失带来了可识别性问题：智能体无法区分随机失败与协调不足。我们将该场景形式化为阈值激活合作多臂赌博机（TAC-MAB），并在集中式和分散式协调下进行分析。我们证明，集中式算法（C-TAC）实现了累积遗憾O(log T)，该遗憾可分解为结构搜索项（捕捉删失反馈下解决可行性问题的代价）和统计监控项（用于价值估计）。随后，我们提出了D-TAC，这是一种分散式事件触发协议，智能体仅在结构信念发生变化时进行同步。实验表明，与集中式基线相比，D-TAC在通信量上减少了23倍，同时通过保守信念融合保持了可行性对齐。这些结果刻画了删失反馈下学习的协调代价，并表明无需持续同步即可实现接近集中式的通信效率。