Learning to Spend: Model Predictive Control for Budgeting under Non-Stationary Returns

2026-04-29

AI Summary

This study addresses the finite-horizon budget allocation problem under non-stationary changes in return efficiency by formulating it as a closed-loop economic control problem. The authors employ a receding-horizon model predictive control (MPC) approach to dynamically optimize budget allocation, accounting for execution noise and operational constraints. Through comparison with reactive strategies, the research demonstrates that non-stationarity alone is insufficient for MPC to outperform reactive methods; MPC achieves significant and sustained superiority only when the return efficiency exhibits predictable structures that the model can effectively capture, thereby enabling advantageous intertemporal trade-offs. In contrast, under scenarios of random drift or stationarity, MPC offers no notable performance advantage over reactive approaches.

Abstract

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.

Problem

• budget allocation
• non-stationary returns
• model predictive control
• economic control
• intertemporal trade-offs

Innovation

• Model Predictive Control
• Budget Allocation
• Non-Stationary Returns
• Intertemporal Trade-offs
• Receding Horizon Control