Strategic Classification from Revealed Preferences (1710.07887v1)

Abstract: We study an online linear classification problem, in which the data is generated by strategic agents who manipulate their features in an effort to change the classification outcome. In rounds, the learner deploys a classifier, and an adversarially chosen agent arrives, possibly manipulating her features to optimally respond to the learner. The learner has no knowledge of the agents' utility functions or "real" features, which may vary widely across agents. Instead, the learner is only able to observe their "revealed preferences" --- i.e. the actual manipulated feature vectors they provide. For a broad family of agent cost functions, we give a computationally efficient learning algorithm that is able to obtain diminishing "Stackelberg regret" --- a form of policy regret that guarantees that the learner is obtaining loss nearly as small as that of the best classifier in hindsight, even allowing for the fact that agents will best-respond differently to the optimal classifier.

• The paper introduces a computationally efficient algorithm that minimizes Stackelberg regret in an online strategic classification setting.
• It establishes convexity conditions for optimization, ensuring tractable solutions even under adversarial agent manipulations.
• The research offers practical insights for building robust classifiers in real-world applications like spam filtering and loan approvals.

Strategic Classification from Revealed Preferences: An Overview

This paper investigates an online linear classification problem characterized by strategic agents who manipulate their features to influence classification outcomes. A learner deploys a classifier, encountering agents who potentially manipulate their features, driven by individual utility functions that are unknown to the learner. Instead, the learner observes the agents' "revealed preferences," which are the manipulated feature vectors. Strategic classification is a game between the learner and the agents, with goals to compute an equilibrium strategy that maximizes utility, specifically in the Stackelberg framework.

Problem Formulation

The learner faces an online classification scenario where agents strategically modify their feature vectors in response to the classifier. Agents are divided into strategic and non-strategic based on their label and adapt their strategies, driven by utility functions incorporating manipulation costs. The learner's challenge is to minimize regret—a specific variation called "Stackelberg regret"—comparing cumulative loss against a hypothetical best classifier in hindsight while accounting for dynamic responses from agents.

Key Contributions and Algorithmic Solutions

The authors propose a computationally efficient learning algorithm guaranteeing diminishing Stackelberg regret even under adversarial conditions. The research advances the understanding of strategic classification by addressing the problem without presupposing knowledge of agents' utility functions or distributions of original features:

1. Convexity Conditions: The paper outlines conditions where the learner's optimization problem remains convex, providing tractable solutions in full information settings. These conditions are satisfied by particular cost function classes, such as squared Mahalanobis distances or any norm-induced metric raised to a power greater than one.
2. Algorithm Innovation: The algorithm leverages revealed preferences in interactions between learner and agents, utilizing a mixture of first-order (gradient-based) methods when agents are non-strategic and zeroth-order methods (bandit-based) when agents are strategic. This approach allows for adaptability and minimized regret—the performance metric being a function of the strategic agent proportion.

Implications and Future Directions

The practical implication of this research lies in improved robustness of classifiers in environments where data manipulation is prevalent, such as spam filtering or loan approvals. The theoretical contributions include enhanced frameworks for learning in strategic contexts, setting grounds for further exploration in non-convex utility function scenarios or imperfect agent responses.

The paper poses future research questions, notably on robust algorithmic approaches when agents display non-convex behaviors or don't execute perfect best responses. Such directions aim to further weaken assumptions around strategic agent modeling, enhancing the applicability in real-world systems where precise agent behavior models are unrealistic.

In summary, this work presents a significant step in strategic classification paradigms, offering nuanced perspectives and tools for learners optimizing under uncertainty posed by strategic agent manipulations. While the proposed solutions and frameworks offer robust initial steps, ongoing enhancements are anticipated to address broader complexities and imperfections in strategic settings.