面向政策的大规模因子实验设计
Policy-Aware Design of Large-Scale Factorial Experiments
AI总结：
本文研究如何在有限预算下设计大规模因子实验，通过两阶段方法集中重叠实验，利用低秩张量建模预期结果，提升组合产品设计的可行性。
摘要：
数字公司经常在共享用户群体上运行大量在线实验。当产品决策是组合形式，如界面元素、流程、信息或激励的组合时，可行干预的数量呈指数增长，而可用流量有限。重叠实验可能产生难以用分散A/B测试处理的交互效应。本文研究如何在非估计每个治疗效应但识别高绩效政策的目标下设计大规模因子实验。我们提出一个两阶段设计，将重叠实验集中为单一因子问题，并将预期结果建模为低秩张量。第一阶段，平台采样干预组合子集，利用张量补全推断未测试组合的性能，并通过估计边际贡献消除弱因子水平。第二阶段，对存活组合应用顺序缩减法以选择最终政策。我们建立了与间隙无关的简单遗憾界和与间隙相关的识别保证，表明相关复杂度与低秩张量的自由度和因子水平间的分离结构有关，而非完整的因子规模。在基于1亿次淘宝交互构建的产品捆绑问题的离线评估中，所提方法在低预算和高噪声设置下显著优于一次性张量补全和无结构最佳臂基准。这些结果展示了集中化、面向政策的实验如何使组合产品设计在平台规模上成为操作可行。
英文摘要：
Digital firms routinely run many online experiments on shared user populations. When product decisions are compositional, such as combinations of interface elements, flows, messages, or incentives, the number of feasible interventions grows combinatorially, while available traffic remains limited. Overlapping experiments can therefore generate interaction effects that are poorly handled by decentralized A/B testing. We study how to design large-scale factorial experiments when the objective is not to estimate every treatment effect, but to identify a high-performing policy under a fixed experimentation budget. We propose a two-stage design that centralizes overlapping experiments into a single factorial problem and models expected outcomes as a low-rank tensor. In the first stage, the platform samples a subset of intervention combinations, uses tensor completion to infer performance on untested combinations, and eliminates weak factor levels using estimated marginal contributions. In the second stage, it applies sequential halving to the surviving combinations to select a final policy. We establish gap-independent simple-regret bounds and gap-dependent identification guarantees showing that the relevant complexity scales with the degrees of freedom of the low-rank tensor and the separation structure across factor levels, rather than the full factorial size. In an offline evaluation based on a product-bundling problem constructed from 100 million Taobao interactions, the proposed method substantially outperforms one-shot tensor completion and unstructured best-arm benchmarks, especially in low-budget and high-noise settings. These results show how centralized, policy-aware experimentation can make combinatorial product design operationally feasible at platform scale.
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