Strategic Classification With Externalities

TL;DR

This work extends strategic classification to settings with inter-agent externalities, modeling the interaction as a Stackelberg game where a learner commits to a classifier f_ω and agents play a simultaneous game whose Nash equilibrium shapes the learner’s loss. Under pairwise symmetric externalities and convex cost structures, the induced inter-agent game is a potential game with a strictly concave potential Φ, yielding a unique Pure Nash Equilibrium (PNE) that can be computed via convex optimization. The authors prove PAC learning guarantees for classifiers trained to minimize loss at the Stackelberg-Nash Equilibrium and show how to differentiate through the equilibrium to enable gradient-based optimization, including explicit treatment of how the equilibrium changes with the classifier parameters. They also illustrate two externality models—Proportional and Congestion Externalities—and validate strategy-aware training on synthetic data with experiments that highlight improved resilience to manipulation compared with non-strategy-aware baselines. Overall, the paper provides theoretical foundations and practical methods for robust classifiers in multi-agent environments where agents’ actions impact one another.

Abstract

We propose a new variant of the strategic classification problem: a principal reveals a classifier, and $n$ agents report their (possibly manipulated) features to be classified. Motivated by real-world applications, our model crucially allows the manipulation of one agent to affect another; that is, it explicitly captures inter-agent externalities. The principal-agent interactions are formally modeled as a Stackelberg game, with the resulting agent manipulation dynamics captured as a simultaneous game. We show that under certain assumptions, the pure Nash Equilibrium of this agent manipulation game is unique and can be efficiently computed. Leveraging this result, PAC learning guarantees are established for the learner: informally, we show that it is possible to learn classifiers that minimize loss on the distribution, even when a random number of agents are manipulating their way to a pure Nash Equilibrium. We also comment on the optimization of such classifiers through gradient-based approaches. This work sets the theoretical foundations for a more realistic analysis of classifiers that are robust against multiple strategic actors interacting in a common environment.

Figures (2)

• Figure 1: Strategic training (red), corresponding strategic validation losses (blue), and strategic validation loss of a baseline classifier trained with truthful/non-strategic reporting (green). We plot the mean losses over 15 random datasets (with 90% confidence interval) vs training epochs.
• Figure 2: Strategic training (red), corresponding strategic validation losses (blue), and strategic validation loss of a classifier trained only considering cost (gray). We plot the mean losses over 15 random datasets (with 90% confidence interval) vs training epochs.

Theorems & Definitions (19)

• Definition 1
• Definition 2
• Theorem 1
• proof
• Theorem 2
• proof
• Lemma 1
• Definition 3
• Theorem 3
• Theorem 4