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

arXiv: https://arxiv.org/abs/2604.27186 · HTML: https://mlsanity.com/paper/2604.27186/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 30 references that are in the map.
- First posted on arXiv 29 Apr 2026.

## Builds on (most cited first, 6 of 6)

- [Real-Time Bidding by Reinforcement Learning in Display Advertising](https://mlsanity.com/paper/1701.02490/) (2017)
- [Online Optimal Control with Linear Dynamics and Predictions: Algorithms and Regret Analysis](https://mlsanity.com/paper/1906.11378/) (2019)
- [A Unified Framework for Marketing Budget Allocation](https://mlsanity.com/paper/1902.01128/) (2019)
- [The Power of Predictions in Online Control](https://mlsanity.com/paper/2006.07569/) (2020)
- [An End-to-End Framework for Marketing Effectiveness Optimization under Budget Constraint](https://mlsanity.com/paper/2302.04477/) (2023)
- [A Field Guide for Pacing Budget and ROS Constraints](https://mlsanity.com/paper/2302.08530/) (2023)

## Abstract (arXiv)

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.