首次建立网络干扰下带宽博弈的后悔与推断精度权衡理论边界
Design-Based Bandits Under Network Interference: Trade-Off Between Regret and Statistical Inference
- 提出设计基础的网络干扰带宽博弈框架，考虑节点间影响
- 构建任意时刻有效的渐近置信序列，实现后悔与推断平衡
- 适合关注多智能体决策中统计推断可靠性的研究者
在具有网络干扰的多臂赌博机（MABNI）中，一个节点的行动会影响其他节点的奖励，形成复杂的依赖关系。现有研究主要关注最小化后悔，但过度追求最优臂会损害对次优臂的推断精度。尽管已有工作尝试在单单元场景中解决这一权衡问题，但在MABNI背景下该挑战更为突出。本文首次在对抗性（设计基础）MABNI设定下，建立了描述后悔最小化与推断准确性之间权衡的理论帕累托前沿。我们进一步提出一种任意时刻有效的渐近置信序列，以及相应的算法 $ exttt{EXP3-N-CS}$，专门用于平衡此场景下的后悔最小化与推断准确性。
原文摘要 · Abstract (English)
In multi-armed bandits with network interference (MABNI), the action taken by one node can influence the rewards of others, creating complex interdependence. While existing research on MABNI largely concentrates on minimizing regret, it often overlooks the crucial concern that an excessive emphasis on the optimal arm can undermine the inference accuracy for sub-optimal arms. Although initial efforts have been made to address this trade-off in single-unit scenarios, these challenges have become more pronounced in the context of MABNI. In this paper, we establish, for the first time, a theoretical Pareto frontier characterizing the trade-off between regret minimization and inference accuracy in adversarial (design-based) MABNI. We further introduce an anytime-valid asymptotic confidence sequence along with a corresponding algorithm, $\texttt{EXP3-N-CS}$, specifically designed to balance the trade-off between regret minimization and inference accuracy in this setting.
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