A Note on Task-Aware Loss via Reweighing Prediction Loss by Decision-Regret

Abstract

In this short technical note we propose a baseline for decision-aware learning for contextual linear optimization, which solves stochastic linear optimization when cost coefficients can be predicted based on context information. We propose a decision-aware version of predict-then-optimize. We reweigh the prediction error by the decision regret incurred by an (unweighted) pilot estimator of costs to obtain a decision-aware predictor, then optimize with cost predictions from the decision-aware predictor. This method can be motivated as a finite-difference, iterate-independent approximation of the gradients of previously proposed end-to-end learning algorithms; it is also consistent with previously suggested intuition for end-to-end learning. This baseline is computationally easy to implement with readily available reweighted prediction oracles and linear optimization, and can be implemented with convex optimization so long as the prediction error minimization is convex. Empirically, we demonstrate that this approach can lead to improvements over a "predict-then-optimize" framework for settings with misspecified models, and is competitive with other end-to-end approaches. Therefore, due to its simplicity and ease of use, we suggest it as a simple baseline for end-to-end and decision-aware learning.

Leaving the Nest: Going beyond Local Loss Functions for Predict-Then-Optimize

“…Multiple authors have suggested learning task-specific loss functions for DFL (Chung et al 2022;Lawless and Zhou 2022;Shah et al 2022). These approaches add learnable parameters to standard loss functions (e.g., MSE) and tune them, such that the resulting loss functions approximate the 'regret' in DQ for 'typical' predictions.…”

“…4. Learning predictive model M ✓ : Train the predictive model M ✓ on the loss functions learned in the previous step, e.g., a random forest (Chung et al 2022), a neural network (Shah et al 2022), or a linear model (Lawless and Zhou 2022). In this paper, we propose two modifications to the metaalgorithm above.…”

“…In this paper, we refer to the broad class of methods used to achieve this goal as Decision-Focused Learning (DFL). Recently, multiple papers have proposed learning task-specific loss functions for DFL (Chung et al 2022;Lawless and Zhou 2022;Shah et al 2022). The intuition for these methods can be summarized in terms of the Anna Karenina principle-while perfect predictions lead to perfect decisions, different kinds of imperfect predictions have different impacts on downstream decision-making.…”

“…However, this doesn't take into account the kinds of predictions that models actually generate and, as a result, can lead to the loss functions being optimized for unrealistic predictions. In contrast, Lawless and Zhou (2022) and Chung et al (2022) use a predictive model trained using MSE to produce a single representative sample that is used to construct a simple loss function. However, this single sample is not sufficient to learn complex loss functions.…”