# Interpretable Optimization: Why and How We Should Explain Optimization Models
## 1 Introduction: Interpretability in Machine Learning and Optimization
### Interpretability in Machine Learning  
In the context of machine learning (ML), interpretability is understood as the highest possible degree of transparency, allowing the user to comprehend the rationale behind the solution proposed by an algorithm, as well as to integrate this rationale with their prior knowledge of the problem. Transparency is a key pillar of artificial intelligence (AI) ethics. [PERSON] et al. [2] extensively reviewed 47 ethics guidelines for AI and found that transparency featured in their practical totality as the only way to guarantee responsibility and avoid serious ethical issues such as bias. As an illustration, the COMPAS (Correctional Offender Management Profiling for Alternative Sanctions) is a clear example of the ethical risks posed by a lack of interpretability in machine learning models [3]. This risk assessment tool, used in the U.S. criminal justice system, was found to exhibit racial bias, assigning disproportionately higher recidivism risk scores to African American defendants compared to white defendants with similar backgrounds. The opacity of the model, which was a black box that only returned a risk score without any justification, made it impossible for defendants, legal professionals, or policymakers to scrutinize or challenge its decisions. This is why transparency and interpretability are essential for the ethical deployment of AI. Without these principles, AI systems may reinforce and exacerbate existing biases, leading to unfair and potentially harmful outcomes. Transparency enables stakeholders to assess whether a model's decisions align with ethical values such as fairness. For instance, in industrial settings, strategic decisions cannot be left to black boxes because important decisions require discussion, agreement, and justification, which cannot be attempted without a decision rationale. How can we be sure that the decision is not merely the result of a flaw in the model, the training data, or a product of overfitting? Only access to decision rationales can mitigate these risks, enabling the responsible and robust use of models. These concerns fostered the development of explainable machine learning (XML) [4], which includes a set of techniques that provide ex-post explanations of model decisions by identifying the most influential variables, thereby improving transparency and trust. The most widely used XML methods include permutation importance and SHapley Additive explanations (SHAP) values, which quantify the contribution of individual variables to predictions [5; 6]. Partial Dependence Plots (PDPs) and Accumulated Local Effects (ALEs) help visualize how specific features influence model outcomes while accounting for data dependencies. Local interpretability methods like LIME (Local Interpretable Model-Agnostic Explanations) assess feature impact by introducing small input perturbations [7], whereas counterfactual explanations determine the minimal changes required to alter a decision, clarifying decision boundaries. Additionally, surrogate models, such as interpretable decision trees, approximate complex models to provide a more accessible understanding of their behavior. Recent developments such as NeuralSens [8] have made substantial progress towards \"opening the black box\" of artificial neural networks, providing insights into their internal processes, which were previously unavailable. These approaches enhance explainability and enable more informed decision-making, but they come with many caveats such as the possibility of \"evil\" tailoring models for a specific post hoc explanation [9]. However, explainability is not enough for many, and greater emphasis should be placed on full interpretability. Interpretable machine learning (IML) produces models capable of generating decision rationales that can be integrated with domain knowledge,along with the proficiency of experts. Full interpretability ensures that AI systems align their decision-making logic with the established expertise of humans and reasoning within a given field.