The streams of research on adversarial examples and counterfactual explanations have largely been growing independently. This has led to several recent works trying to elucidate their similarities and differences. Most prominently, it has been argued that adversarial examples, as opposed to counterfactual explanations, have a unique characteristic in that they lead to a misclassification compared to the ground truth. However, the computational goals and methodologies employed in existing counterfactual explanation and adversarial example generation methods often lack alignment with this requirement. Using formal definitions of adversarial examples and counterfactual explanations, we introduce non-adversarial algorithmic recourse and outline why in high-stakes situations, it is imperative to obtain counterfactual explanations that do not exhibit adversarial characteristics. We subsequently investigate how different components in the objective functions, e.g., the machine learning model or cost function used to measure distance, determine whether the outcome can be considered an adversarial example or not. Our experiments on common datasets highlight that these design choices are often more critical in deciding whether recourse is non-adversarial than whether recourse or attack algorithms are used. Furthermore, we show that choosing a robust and accurate machine learning model results in less adversarial recourse desired in practice.
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