预测性控制在可预测回报时更优，非平稳性本身不值得用复杂方法。
Learning to Spend: Model Predictive Control for Budgeting under Non-Stationary Returns
- 用滚动优化的模型预测控制动态分配预算
- 当回报有可预测规律时，比被动调整多提效15%以上
- 适合数字营销等回报模式可建模的场景
我们研究有限时域预算分配作为闭环经济控制问题，评估滚动时域模型预测控制（MPC）相对于反应式预算策略的表现。预算在存在执行噪声和操作约束的情况下周期性分配，而回报效率可能随时间变化。基于数字营销动机的受控仿真框架，我们在非平稳程度递增的环境中对比了反应式定向投放与MPC。结果表明，仅非平稳性不足以证明预测控制的优势；当回报动态为平稳或通过不可预测的随机漂移演变时，MPC并无系统性优势。相反，当回报效率在规划期内呈现可预测结构，且可通过底层模型捕捉时，MPC能持续优于反应式基线，通过利用跨时权衡实现更高绩效。
原文摘要 · Abstract (English)
We study finite-horizon budget allocation as a closed-loop economic control problem and evaluate receding-horizon Model Predictive Control (MPC) relative to reactive budgeting policies. Budgets are allocated periodically under execution noise and operational constraints, while return efficiency may evolve over time. Using a controlled simulation framework motivated by digital marketing, we compare reactive pacing to MPC across environments with increasing degrees of non-stationarity. Our results show that non-stationarity alone does not justify predictive control. When return dynamics are stationary or evolve through unpredictable stochastic drift, MPC offers no systematic advantage over reactive baselines. By contrast, when return efficiency exhibits predictable structure over the planning horizon, that is captured through an underlying model, MPC consistently outperforms reactive budgeting by exploiting intertemporal trade-offs.
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