用事后后悔值评估营销预算分配效率,判断过去决策是否最优。
Auditing Marketing Budget Allocation with Hindsight Regret

- 基于历史数据估算不同场景的投入产出关系
- 通过约束优化计算理想分配方案,得出预期提升幅度
- 适合无法实时实验的团队做事后决策复盘
组织在运营约束下进行战略预算分配,但常缺乏系统方法来判断实际分配是否接近事后最优。本文提出一种基于事后后悔值的回溯审计框架:定义后悔值为实际分配与满足约束条件下的基准分配之间的机会成本。该框架从历史日志中估计分场景的投入-响应函数,通过约束优化计算可行的回顾性分配,并利用蒙特卡洛方法传播不确定性,生成后悔值分布、期望提升和改进概率等统计量。该方法将分配低效性与响应面估计不确定性区分开。在真实营销预算日志上的实验表明,该框架可提供可解释的后验诊断,揭示分配灵活性与可检测性之间的权衡:适度调整通常能捕获大部分可测量收益,而大幅调整则进入支持度弱的区域,不确定性更高。该方法适用于在线实验成本高或不可行时的历史决策审计。
原文摘要 · Abstract (English)
Organizations routinely make strategic budget allocations under operational constraints, but often lack a principled way to assess whether realized allocations were close to the best feasible choices in hindsight. We present a retrospective auditing framework based on hindsight regret, defined as the opportunity cost of the realized allocation relative to a constraint-faithful benchmark under the same budget and stability guardrails. The framework estimates regime-specific spend--response functions from historical logs, computes feasible hindsight allocations via constrained optimization, and propagates uncertainty through Monte Carlo evaluation to produce regret distributions, expected lift, and probability-of-improvement summaries. This separates allocation inefficiency from uncertainty in the estimated response surfaces. Experiments on real marketing allocation logs show that the framework yields interpretable post-hoc diagnostics and reveals a practical trade-off between allocation flexibility and detectability: moderate feasible reallocations often capture most measurable gain, while larger shifts move into weak-support regions with higher uncertainty. The result is a practical method for auditing historical budget decisions when online experimentation is costly or infeasible.
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