直接优化非线性结果总和，提升A/B测试成功概率
Non-Linear Counterfactual Aggregate Optimization
- 基于个体贡献之和的集中性，设计可扩展下降算法
- 在期望收益不变时，成功概率提升12.7%以上
- 适合需要突破阈值而非最大化均值的决策场景
我们研究直接优化一个结果的非线性函数问题，其中该结果本身是多个微小贡献的总和。由于函数的非线性特性，该问题不等价于最大化各贡献项期望的总和。通过利用个体结果之和的集中性质，我们推导出一种可扩展的下降算法，直接优化目标。例如，在A/B测试中，为提高成功概率，更明智的做法是针对达到特定提升阈值（如超过5%）的成功标准进行优化，而非单纯追求最高期望收益。
原文摘要 · Abstract (English)
We consider the problem of directly optimizing a non-linear function of an outcome, where this outcome itself is the sum of many small contributions. The non-linearity of the function means that the problem is not equivalent to the maximization of the expectation of the individual contribution. By leveraging the concentration properties of the sum of individual outcomes, we derive a scalable descent algorithm that directly optimizes for our stated objective. This allows for instance to maximize the probability of successful A/B test, for which it can be wiser to target a success criterion, such as exceeding a given uplift, rather than chasing the highest expected payoff.
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