[Paper Review] A Note on Task-Aware Loss via Reweighing Prediction Loss by Decision-Regret

Connor Lawless, Angela Zhou|arXiv (Cornell University)|Nov 9, 2022

Age of Information Optimization4 citations

TL;DR

This paper proposes a simple, computationally efficient baseline for decision-aware learning in contextual linear optimization by reweighting prediction loss using decision regret from a pilot estimator. The method improves decision regret over standard predict-then-optimize, especially under model misspecification, and performs competitively with complex end-to-end methods like SPO+ while being easy to implement with standard regression and optimization oracles.

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.

Motivation & Objective

• To address the gap between standard prediction-focused models and decision-aware optimization in contextual linear stochastic optimization.
• To propose a computationally tractable method that incorporates decision regret into prediction loss without complex end-to-end backpropagation.
• To provide a practical baseline for end-to-end learning that is easy to implement and consistent with existing intuition about task-aware learning.
• To empirically evaluate whether reweighting prediction error by decision regret leads to improved decision regret compared to standard predict-then-optimize.

Proposed method

• Reweigh the mean-squared error (MSE) of a cost predictor by the decision regret obtained from a pilot (unweighted) estimator of costs.
• Use the reweighted MSE as a surrogate loss for training a predictor, which is then used in a predict-then-optimize framework.
• Apply iterative reweighting via alternating optimization between updating the predictor and reweighting data points based on decision regret.
• The method is motivated as a zeroth-order, iterate-independent approximation to the gradients of end-to-end decision-aware learning objectives.
• It leverages standard convex optimization oracles for prediction and linear programming for decision-making.
• The approach is implemented with a mixture hyperparameter ν to balance uniform weighting and regret-based weighting.

Experimental results

Research questions

• RQ1 Can reweighting prediction loss by decision regret lead to better decision regret than standard predict-then-optimize in misspecified models?
• RQ2 How does the proposed method compare in performance to established end-to-end approaches like SPO+?
• RQ3 Does iterative reweighting improve performance, or does convergence occur quickly after one iteration?
• RQ4 Why does reweighting fail to improve predictions when using nonparametric models like random forests?
• RQ5 Is the method a viable, simple baseline for decision-aware learning in linear optimization?

Key findings

• For misspecified models, the reweighted MSE approach reduces test decision regret by 30–60% compared to standard predict-then-optimize, especially as training data increases.
• The method achieves performance comparable to SPO+ in the shortest path experiment, outperforming predict-then-optimize and matching SPO+ in normalized out-of-sample regret.
• Iterative reweighting (K > 1) provides negligible improvement, indicating convergence after a single reweighting step.
• With random forest predictors, reweighting has minimal effect, as expected due to the model’s nonparametric flexibility and robustness to misspecification.
• The method is computationally efficient and easy to implement using standard regression and linear optimization oracles, making it a strong practical baseline.