arXiv:2605.11191stat.MLcs.LG2026-05

在未知网络干扰下,自适应优化个体治疗分配并同时学习干扰结构。

Adaptive Policy Learning Under Unknown Network Interference

论文配图:Adaptive Policy Learning Under Unknown Network Interference
图 1 · 摘自论文原文
  • 联合使用吉布斯采样与汤普森采样,同步学习干扰网络与最优策略。
  • 理论证明贝叶斯后悔上界为√(nT·B log(en/B)),实测表现接近该速率。
  • 适用于真实网络场景,可准确估计直接、间接和总效应,适合因果推断研究者。

在未知网络干扰下的自适应实验需解决两个耦合问题:(i) 学习单元间干扰的潜在动态;(ii) 利用这些动态优化治疗分配以最大化累积结果(如收入)。现有方法要么假设干扰网络完全已知,要么通过粗粒度聚类随机化绕过网络。我们提出一种汤普森采样算法,结合吉布斯采样,同时学习干扰网络并自适应优化个体级治疗分配。该算法输出优化的治疗策略及干扰网络估计,支持下游因果分析(如直接、间接和总效应估计)。对于加性溢出模型,总收益是治疗向量的线性函数,系数由 n 维隐含得分决定。我们证明精确后验采样的贝叶斯后悔上界为 √(nT·B log(en/B));实证中,基于吉布斯的近似采样器表现出与该速率一致的后悔,即使在加性溢出假设不成立时仍保持次线性。针对一般邻域干扰(无此简化),我们分析了一种探索-然后承诺变体,图发现成本为 O(n² log T)。信息论下界 Ω(n log T) 与此互补。实测显示,相比基线方法,本方法在后悔上降低一个数量级以上。在两个真实网络数据集上,算法实现次线性后悔,并获得相对真实值的小均方根误差效应估计。

原文摘要 · Abstract (English)

Adaptive experimentation under unknown network interference requires solving two coupled problems: (i) learning the underlying dynamics of interference among units and (ii) using these dynamics to inform treatment allocation in order to maximize a cumulative outcome of interest (e.g. revenue). Existing adaptive experimentation methods either assume the interference network is fully known or bypass the network by operating on coarse cluster-level randomizations. We develop a Thompson sampling algorithm that jointly learns the interference network and adaptively optimizes individual-level treatment allocations via a Gibbs sampler. The algorithm returns both an optimized treatment policy and an estimate of the interference network; the latter supports downstream causal analyses such as estimation of direct, indirect, and total treatment effects. For additive spillover models, we show that total reward is linear in the treatment vector with coefficients given by an $n$-dimensional latent score. We prove a Bayesian regret bound of order $\sqrt{nT \cdot B \log(en/B)}$ for exact posterior sampling; empirically, our Gibbs-based approximate sampler achieves regret consistent with this rate and remains sublinear when the additive spillovers assumption is violated. For general Neighborhood Interference, where this reduction is unavailable, we analyze an explore-then-commit variant with $O(n^2 \log T)$ graph-discovery cost. An information-theoretic $Ω(n \log T)$ lower bound complements both results. Empirically, our method achieves more than an order-of-magnitude reduction in regret in head-to-head comparisons. On two real-world networks, the algorithm achieves sublinear regret and yields downstream effect estimates with small RMSE relative to the truth.

自适应实验网络干扰因果推断贝叶斯优化

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