Modeling Robustness in Decision-Focused Learning as a Stackelberg Game

Predict-then-optimize is a common paradigm for optimization tasks situated in incomplete informational settings, in which an agent estimates missing parameters and then optimizes over these predicted parameters. One proposed improvement to this predict-thenoptimize framework is decision-focused learning, which establishes an end-to-end learning pipeline, allowing a predictive model to be tailored to the particular optimization task. The behavior of this predict-then-optimize framework in the presence of noise, however, is not well-understood. This is problematic because many data collection and annotation systems are inherently noisy, and the introduction of such noise could lead to poor downstream optimization. In this work, we aim to present results on robustness to label noise in decision-focused learning and traditional predictthen-optimize tasks using a Stackelberg game as the underlying framework of explanation. Our results suggest that playing the Stackelberg game in anticipation of label noise yields robustness in the predict-then-optimize framework at large, and that the optimal decision-focused learning Stackelberg solution continues to outperform the optimal traditional predict-then-optimize Stackelberg solution.