The Price of Looking Ahead: Decision-Focused Learning for Multistage Decision-Making

Decision-focused learning trains predictors for downstream optimization, but most existing methods address static problems or assume a fixed planning horizon. However, the look-ahead horizon is central to multistage decision-making: short horizons limit compounding forecast errors but encourage myopic actions, whereas long horizons provide foresight but incur greater prediction error. We formalize this trade-off for multistage predict-then-optimize systems, decomposing regret into truncation bias and cascading forecast error. Theoretically, we reveal how system dynamics, forecast accuracy, and horizon length govern these components, explaining why an intermediate horizon can outperform myopic and full-horizon planning. Empirically, experiments on synthetic and real-world energy benchmarks corroborate the theory, revealing U-shaped regret across planning horizons.