Minimax Group Fairness in Strategic Classification

TL;DR

This work formalizes a fairness-aware Stackelberg game between a population of agents consisting of several groups, with each group having its own cost function, and a learner in the agnostic PAC setting in which the learner is working with a hypothesis class $\mathcal{H}$.

Abstract

In strategic classification, agents manipulate their features, at a cost, to receive a positive classification outcome from the learner's classifier. The goal of the learner in such settings is to learn a classifier that is robust to strategic manipulations. While the majority of works in this domain consider accuracy as the primary objective of the learner, in this work, we consider learning objectives that have group fairness guarantees in addition to accuracy guarantees. We work with the minimax group fairness notion that asks for minimizing the maximal group error rate across population groups. We formalize a fairness-aware Stackelberg game between a population of agents consisting of several groups, with each group having its own cost function, and a learner in the agnostic PAC setting in which the learner is working with a hypothesis class H. When the cost functions of the agents are separable, we show the existence of an efficient algorithm that finds an approximately optimal deterministic classifier for the learner when the number of groups is small. This algorithm remains efficient, both statistically and computationally, even when H is the set of all classifiers. We then consider cost functions that are not necessarily separable and show the existence of oracle-efficient algorithms that find approximately optimal randomized classifiers for the learner when H has finite strategic VC dimension. These algorithms work under the assumption that the learner is fully transparent: the learner draws a classifier from its distribution (randomized classifier) before the agents respond by manipulating their feature vectors. We highlight the effectiveness of such transparency in developing oracle-efficient algorithms. We conclude with verifying the efficacy of our algorithms on real data by conducting an experimental analysis.

Figures (6)

• Figure 1: The max group error of the two baselines and our method, in the test time ( Ts), on the (a) COMPAS, (b) Credit, (c) Communities, and (d) Heart datasets with an equal budget $\tau$ for all agents.
• Figure 2: The plots show the convergence of our algorithm during the training ( Tr) phase across (a) COMPAS, (b) Credit, (c) Communities, and (d) Heart, with $\tau = 1$, and the number of iterations is $T = 3000$.
• Figure 3: The performance of the baselines and our approach on the Heart dataset across different manipulation budget profiles for groups.
• Figure 4: The performance of the baselines and our approach on the Credit dataset across different values of manipulation budgets for groups.
• Figure 5: The performance of the baselines and our approach on the COMPAS dataset across different values of manipulation budgets for groups.

Theorems & Definitions (44)

• Definition 2.1: Strategic Error Rates
• Definition 2.2: Strategic Minimax Fairness
• Definition 2.3: The Fairness-aware Strategic Game
• Definition 2.4: VC dimension
• Lemma 2.5: Sauer's Lemma
• Theorem 2.6: Generalization for VC Classes
• Definition 2.7: Strategic VC Dimension sundaram2023pac
• Definition 2.8: Approximate Equilibrium
• Theorem 2.9: No-Regret Dynamics fs1996
• Lemma 3.2: Sufficiency of Optimizing over $\mathcal{F}$