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

TL;DR

This paper evaluates Model Predictive Control (MPC) for budget allocation in non-stationary environments, finding it advantageous only when return dynamics are predictable over the planning horizon.

Contribution

It demonstrates that MPC's effectiveness depends on the predictability of return efficiency, providing insights into when predictive control outperforms reactive policies.

Findings

MPC does not outperform reactive policies in purely stochastic or stationary environments.

Predictable return dynamics enable MPC to outperform reactive baselines.

Non-stationarity alone does not justify the use of MPC.

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.