Decision-Driven Regularization: A Blended Model for Learning and Optimization

arXiv:2608.15124v1 Announce Type: new Abstract: In contextual optimization, the decision-maker seeks optimal decisions to minimize a cost function, that varies based on observed features. This context is common in many business applications ranging from on-demand delivery and retail operations to portfolio optimization and inventory management. In this paper, we study the learning and optimization approach, which first learns how outcomes result from the features, and then selects optimal decisions based on these outcomes. We focus on the integrated learning and optimization literature, and identify that a lack of control for prediction accuracy can lead to overfitting and a loss of decision effectiveness against simple separate learning and optimization models. Instead, we propose a bi-objective formulation that balances prediction accuracy and cost minimization, termed decision-driven regularization. It also addresses ambiguity in the definition of the cost function via a surrogate that depends on a new hyperparameter. We additionally show that alternative perspectives for formulating the problem, namely robust optimization and regret minimization, lead to models that are closely related to our proposed model. As a consequence, our framework generalizes models such as SPO+. Our model is shown to be numerically superior to other benchmarks, such as OLS, Random Forest, XGBoost, SPO+, Perturbation Gradient, and Learning and Rank, in our synthetic studies.

Abstract:In contextual optimization, the decision-maker seeks optimal decisions to minimize a cost function, that varies based on observed features. This context is common in many business applications ranging from on-demand delivery and retail operations to portfolio optimization and inventory management. In this paper, we study the learning and optimization approach, which first learns how outcomes result from the features, and then selects optimal decisions based on these outcomes. We focus on the integrated learning and optimization literature, and identify that a lack of control for prediction accuracy can lead to overfitting and a loss of decision effectiveness against simple separate learning and optimization models. Instead, we propose a bi-objective formulation that balances prediction accuracy and cost minimization, termed decision-driven regularization. It also addresses ambiguity in the definition of the cost function via a surrogate that depends on a new hyperparameter. We additionally show that alternative perspectives for formulating the problem, namely robust optimization and regret minimization, lead to models that are closely related to our proposed model. As a consequence, our framework generalizes models such as SPO+. Our model is shown to be numerically superior to other benchmarks, such as OLS, Random Forest, XGBoost, SPO+, Perturbation Gradient, and Learning and Rank, in our synthetic studies.

Machine Learning (cs.LG); Optimization and Control (math.OC)

arXiv:2608.15124 [cs.LG]

(or arXiv:2608.15124v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2608.15124 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

analiza aiqbench

Decision-Driven Regularization: A Blended Model for Learning and Optimization

Subiecte conexe