Managing Solution Stability in Decision-Focused Learning with Cost Regularization
This work addresses a specific bottleneck in decision-focused learning for combinatorial optimization, making it incremental.
The paper tackled the problem of solution instability in decision-focused learning caused by fluctuations in perturbation intensity during training, and proposed a cost regularization method that improved robustness and reliability, as shown in extensive numerical experiments.
Decision-focused learning integrates predictive modeling and combinatorial optimization by training models to directly improve decision quality rather than prediction accuracy alone. Differentiating through combinatorial optimization problems represents a central challenge, and recent approaches tackle this difficulty by introducing perturbation-based approximations. In this work, we focus on estimating the objective function coefficients of a combinatorial optimization problem. Our study demonstrates that fluctuations in perturbation intensity occurring during the learning phase can lead to ineffective training, by establishing a theoretical link to the notion of solution stability in combinatorial optimization. We propose addressing this issue by introducing a regularization of the estimated cost vectors which improves the robustness and reliability of the learning process, as demonstrated by extensive numerical experiments.