This work develops an inverse optimization approach to jointly learn the decision-maker's preferences and the decision rules governing their choices, which leads to better predictions and greater flexibility in capturing and replicating expert decision making.
Abstract
Understanding how experts make decisions and being able to transfer that knowledge is important, especially in complex engineering applications. It is highly valuable for training novices, improving the performance of human-machine systems, and potentially enabling fully autonomous systems that perform as well as human experts. However, an expert's decision-making strategy, developed through years of experience, is often not directly accessible, since the implicit preferences and decision rules involved can be difficult to specify explicitly. This has motivated the use of observed decisions made by the expert to learn an interpretable model that captures the expert's decision-making process. In this work, we develop an inverse optimization approach to jointly learn the decision-maker's preferences (or perceived costs) and the decision rules governing their choices. We demonstrate the general applicability of our approach using three case studies that consider a shift assignment problem, a production planning problem, and a real-world routing problem, respectively. Across these case studies, modeling both perceived costs and decision rules leads to better predictions, highlighting the value of the proposed framework and its greater flexibility in capturing and replicating expert decision making.
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 biobjective 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 ordinary least squares, random forest, XGBoost, SPO+, perturbation gradient, and learning and rank, in our synthetic studies.
History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis.
Funding: The research of Q. Tang is funded in part by the Ministry of Education, Singapore [Tier 1 Grant RG47/24] and the National Natural Science Foundation of China [Grant 72271147]. The research of X. Zhang is supported by the National Natural Science Foundation of China [Grant 72501273], the Anhui Provincial Natural Science Foundation [Grant 2408085QG222], and the Fundamental Research Funds for the Central Universities [Grant BJ2040160100].
Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0930 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0930 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .
G. Loke, Qinshen Tang, Yangge Xiao et al.· INFORMS journal on computing· 0 citations
Production planning in the manufacturing industry often relies on the use of optimization models, but defining an appropriate objective function can be a challenge. In practice, planners must balance competing goals, manage uncertainty, and account for qualitative business preferences that are difficult to quantify. As a result, many optimization models fail to match expert behavior, limiting trust and adoption. In this work, we propose a data-driven inverse optimization framework to infer the objective function implicitly captured in expert planners'decisions. We formulate the production planning problem as a mixed-integer linear program, where the unknown objective function is represented as a weighted sum of hypothesized cost terms. A suboptimality-loss-based inverse optimization method is then applied to learn the objective weights from historical production plans. The proposed approach is applied to a real industrial case provided by Dow, where the inferred weights reveal that avoiding inventory shortages and maintaining consistent cycle lengths dominate the planners'decision-making. Time- and product-dependent extensions further improve predictive accuracy and uncover evolving priorities. Expert interviews confirm the practical validity of these insights. Overall, this study shows that inverse optimization can transform tacit human expertise into interpretable models, enabling more accurate and trusted decision-support tools for complex industrial systems.
Shivi Dixit, Rishabh Gupta, Adam Kelloway et al.· Chemical engineering researc...· 0 citations
It is shown that a key factor is the error correlation structure between human and AI predictions, and when the AI's prediction errors are negatively correlated with those of the human, the decision maker can construct robust strategies which guarantee improvements in expected utility.
Interactive multi-criterion decision-making (iMCDM) procedures rely on a human decision-maker (DM) to iteratively provide preferences, so scalarized subproblems can move toward a preferred Pareto-optimal solution. This human-in-the-loop nature makes systematic benchmarking difficult, as preference information and interaction patterns vary across individuals and problems. To overcome this limitation and to enable computationally-oriented researchers to contribute more profoundly in the MCDM field, we introduce a Machine-based Decision Maker (Machine-DM) that replaces human DMs with pre-trained machine learning models capable of performing the key iMCDM tasks automatically. The Machine-DM predicts objective classifications, such as which objectives should be improved, relaxed, fixed, or allowed to vary and generates corresponding bounding parameters without requiring knowledge of the true target preferred solution. Using this Machine-DM, we develop machine-based versions of four well-known iMCDM procedures: STEM, GUESS, STOM, and NIMBUS. We further propose a set of performance metrics designed to evaluate performance of these iMCDM procedures. Using the Machine-DM concept we also propose a Bench-iMCDM framework for benchmarking iMCDM procedures. Applications to test and engineering problems demonstrate the usefulness of Machine-DM and highlight its potential to serve as a unified framework for comparing a broad class of iMCDM procedures and also to develop new ones.
Deepanshu Yadav, Kalyanmoy Deb· Annual Conference on Genetic...· 2 citations
Interactive multi-criterion decision-making (iMCDM) procedures allow a humam decision-maker (DM) to iteratively adjusts preferences—via objective classification, reference points/directions, or weights—and solves a scalarized problem until a satisfactory Paretooptimal solution is obtained. However, benchmarking a iMCDM procedure remains challenging due to involvement of human DM in making decisions resulting in different solutions. To address this challenge, this paper proposes a stochastic machine learning-based decision-maker: pMachine-DM, which emulates human preference articulation using two stochastic ANNs. The first ANN classifies all objectives according to their desired improvement, relaxation, or satisfaction, while the second ANN predicts the associated bounding parameters. The proposed pMachine-DM is implemented with a specific iMCDM procedure - STEP method. The effectiveness of the approach is demonstrated on four benchmark and four engineering problems. The proposed pMachine-DM is generic and can be integrated with other iMCDM procedures, enabling systematic and reproducible benchmarking without involving human DMs.
Deepanshu Yadav, Kalyanmoy Deb· Proceedings of the Genetic a...· 1 citation
Many operational decisions require solving a linear program whose cost vector is unknown at decision time and must be predicted from contextual information. Because prediction and decision are only weakly aligned, the emerging integrated learning and optimization (ILO) paradigm trains the predictor through the downstream problem, judging a prediction by the decision it induces. However, predictions are inevitably imprecise, so robustness often enters the decision stage. To address this issue, we propose an integrated learning and robust optimization (ILRO) framework, where a robust decision problem is used both to define the training problem (termed the RSPO loss problem), and to produce the deployed decision. Thus, this framework simultaneously achieves both robustness and learning-decision alignment. To tackle its computational challenges, we develop a convex surrogate, RSPO+, and characterize when it is Fisher consistent. Moreover, the RSPO loss possesses informative gradients, allowing us to develop first-order computational methods. We also derive finite-sample excess risk bounds for both RSPO and RSPO+ predictors. Numerical experiments on transportation and portfolio problems, in comparison with multiple benchmarks, show the advantage in decision quality of the proposed framework. The gain is more pronounced for scenarios with limited samples, high-dimensional decisions, and model misspecification.
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