Strategic Classification (1506.06980v2)

Abstract: Machine learning relies on the assumption that unseen test instances of a classification problem follow the same distribution as observed training data. However, this principle can break down when machine learning is used to make important decisions about the welfare (employment, education, health) of strategic individuals. Knowing information about the classifier, such individuals may manipulate their attributes in order to obtain a better classification outcome. As a result of this behavior---often referred to as gaming---the performance of the classifier may deteriorate sharply. Indeed, gaming is a well-known obstacle for using machine learning methods in practice; in financial policy-making, the problem is widely known as Goodhart's law. In this paper, we formalize the problem, and pursue algorithms for learning classifiers that are robust to gaming. We model classification as a sequential game between a player named "Jury" and a player named "Contestant." Jury designs a classifier, and Contestant receives an input to the classifier, which he may change at some cost. Jury's goal is to achieve high classification accuracy with respect to Contestant's original input and some underlying target classification function. Contestant's goal is to achieve a favorable classification outcome while taking into account the cost of achieving it. For a natural class of cost functions, we obtain computationally efficient learning algorithms which are near-optimal. Surprisingly, our algorithms are efficient even on concept classes that are computationally hard to learn. For general cost functions, designing an approximately optimal strategy-proof classifier, for inverse-polynomial approximation, is NP-hard.

• The paper introduces a Stackelberg game model where the Jury and Contestant interact to formalize gaming in classifiers.
• It develops efficient learning algorithms for separable cost functions that maintain near-optimal accuracy under strategic manipulation.
• It demonstrates that designing robust classifiers for general cost functions is NP-hard, highlighting significant computational challenges.

Overview of Strategic Classification

The paper "Strategic Classification" by Moritz Hardt, Nimrod Megiddo, Christos Papadimitriou, and Mary Wootters explores the intersection of machine learning and game theory in the context of strategic manipulation, often referred to as "gaming." This paper is situated within the broader field of adversarial machine learning, focusing on the challenges that arise when individuals consciously adjust their data to influence classifier outputs. The primary aim is to design classifiers that are robust against such strategic actions.

Key Concepts and Contributions

The central framework of the paper models classification as a sequential game between two entities—the "Jury" and the "Contestant." The Jury designs a classifier, whereas the Contestant modifies his inputs to achieve a more favorable classification, incurring costs as defined by a cost function. The interaction is rooted in achieving a strategic equilibrium where both parties optimize their respective objectives given the strategies of the other.

Key contributions of this paper include:

1. Formalizing Gaming in Classification: The paper introduces a theoretical foundation to quantify and understand gaming within machine learning models, offering a framework based on Stackelberg competition—a sequential game structure—where the Jury (strategic classifier) must anticipate and counteract the Contestant's manipulations.
2. Development of Robust Learning Algorithms: For a natural class of cost functions (separable cost functions), the authors present efficient algorithms that approach the theoretical optimal classification accuracy even against gaming.
3. Complexity Insights: The paper demonstrates that for general cost functions, designing an approximately optimal classifier is NP-hard, specifically when attempting to reach results close to the theoretical maximum accuracy within inverse-polynomial approximation.
4. Experimental Validation: Through empirical tests on real-world data (Brazilian social network data), the methodology outperforms traditional classifiers like SVM, especially under conditions where individuals can game the classifier even slightly.

Theoretical and Practical Implications

The theoretical contributions of the paper extend the existing machine-learning paradigms by embedding strategic behaviors into the learning process. This work challenges the standard assumption that test data distributions do not change due to manipulations, which is often violated in practical applications like credit scoring or spam detection.

Practically, this research suggests avenues for enhancing the robustness of machine learning systems deployed in high-stakes domains, such as employment or college admissions, where strategic manipulations are prevalent. The deployment of classifiers designed with strategic robustness in mind could lead to fairer and more resilient decision-making processes.

Future Directions

Potential future work could explore other types of cost functions beyond separable ones and investigate computational methods to efficiently handle higher separability dimensions or large feature spaces. Additionally, extending the strategic model to multi-agent settings or environments with incomplete information poses an important avenue for further research. Such explorations could enhance strategic classification's applicability in dynamic, real-world scenarios where multiple parties contend with one another.

In summary, the paper advances the understanding of classifier gaming and contributes robust strategies to counteract it, bridging a critical gap between theoretical machine learning and practical considerations in adversarial contexts. This work lays groundwork for developing classifiers more resilient to strategic manipulations, improving their reliability in socially impactful applications.