Pigeonhole Design: Balancing Sequential Experiments from an Online Matching Perspective
鸽巢设计：从在线匹配视角平衡序贯实验AI 解读 ↓
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鸽巢设计：从在线匹配视角平衡序贯实验
- 研究问题
- 当在线实验参与者依次到达且必须立即分组时，如何平衡协变量，并最小化处理组与对照组之间基于最优匹配定义的差异？
- 方法与思路
- 作者先将协变量空间划分为多个鸽巢，再在各鸽巢内平衡处理和对照人数，分析理论表现并与配对及完全随机设计比较。
- 材料陈述的贡献
- 摘要称识别出鸽巢设计更有利的场景，并在使用 Yahoo! 数据的模拟中报告，平均处理效应估计方差降低 10.2%。
- 阅读关注点
- 应核对协变量分区、到达过程与即时分配规则、理论比较的条件，以及方差下降所对应的基准设计、估计量和模拟场景。
- 阅读边界
- 这是 arXiv 预印本，不能据此确认同行评审或期刊接收；10.2% 来自所述模拟，摘要未说明具体比较基准，不能视为普遍收益。
原文摘要
Practitioners and academics have long appreciated the benefits of covariate balancing when they conduct randomized experiments. For web-facing firms running online A/B tests, however, it still remains challenging in balancing covariate information when experimental subjects arrive sequentially. In this paper, we study an online experimental design problem, which we refer to as the "Online Blocking Problem." In this problem, experimental subjects with heterogeneous covariate information arrive sequentially and must be immediately assigned into either the control or the treated group. The objective is to minimize the total discrepancy, which is defined as the minimum weight perfect matching between the two groups. To solve this problem, we propose a randomized design of experiment, which we refer to as the "Pigeonhole Design." The pigeonhole design first partitions the covariate space into smaller spaces, which we refer to as pigeonholes, and then, when the experimental subjects arrive at each pigeonhole, balances the number of control and treated subjects for each pigeonhole. We analyze the theoretical performance of the pigeonhole design and show its effectiveness by comparing against two well-known benchmark designs: the match-pair design and the completely randomized design. We identify scenarios when the pigeonhole design demonstrates more benefits over the benchmark design. To conclude, we conduct extensive simulations using Yahoo! data to show a 10.2% reduction in variance if we use the pigeonhole design to estimate the average treatment effect.