Learning to Spend: Model Predictive Control for Budgeting under Non-Stationary Returns
New study reveals when MPC outperforms reactive budgeting in digital marketing.
A new arXiv paper from researchers Nilavra Pathak, Smriti Shyamal, Prasant Mhasker, and Christopher Swartz tackles a core question in automated budgeting: when does predictive control actually beat simple reactive strategies? Their work, titled 'Learning to Spend: Model Predictive Control for Budgeting under Non-Stationary Returns,' frames budget allocation as a closed-loop economic control problem. They compare receding-horizon Model Predictive Control (MPC) against reactive pacing policies in a controlled simulation environment modeled after digital marketing.
The study's key insight is that non-stationarity alone does not justify the complexity of MPC. When return dynamics are stationary or evolve through unpredictable stochastic drift, MPC offers no systematic advantage over reactive baselines. However, when return efficiency follows a predictable structure captured by an underlying model, MPC consistently outperforms by exploiting intertemporal trade-offs. This finding has practical implications for adtech and marketing teams: investing in predictive models only pays off when you can reliably forecast how returns will change over the campaign period. The 8-page paper (no figures) is available on arXiv (2604.27186) in the Systems and Control category, with cross-listing to AI, ML, and Portfolio Management.
- MPC only outperforms reactive pacing when return efficiency has predictable structure over the planning horizon.
- Under stationary or stochastic drift, reactive baselines match MPC — no systematic advantage.
- The simulation framework is motivated by digital marketing budget allocation with execution noise and operational constraints.
Why It Matters
For marketers and budget optimizers: predictive control isn't a silver bullet — model structure matters.