Desirable Effort Fairness and Optimality Trade-offs in Strategic Learning

Abstract

Strategic learning studies how decision rules interact with agents who may strategically change their inputs/features to achieve better outcomes. In standard settings, models assume that the decision-maker's sole scope is to learn a classifier that maximizes an objective (e.g., accuracy) assuming that agents best respond. However, real decision-making systems' goals do not align exclusively with producing good predictions. They may consider the external effects of inducing certain incentives, which translates to the change of certain features being more desirable for the decision maker. Further, the principal may also need to incentivize desirable feature changes fairly across heterogeneous agents. How much does this constrained optimization (i.e., maximize the objective, but restrict agents' incentive disparity) cost the principal? We propose a unified model of principal-agent interaction that captures this trade-off under three additional components: (1) causal dependencies between features, such that changes in one feature affect others; (2) heterogeneous manipulation costs between agents; and (3) peer learning, through which agents infer the principal's rule. We provide theoretical guarantees on the principal's optimality loss constrained to a particular desirability fairness tolerance for multiple broad classes of fairness measures. Finally, through experiments on real datasets, we show the explicit tradeoff between maximizing accuracy and fairness in desirability effort.

Figures (5)

• Figure 1: Examples of $\beta$-fair spaces in $2$ dimensions that satisfy Properties \ref{['property:polyhedron']} (feasible region polyhedral), \ref{['property:ellipsoidal']} ($\beta$-fair space ellipsoidal), and/or \ref{['property:internal_ellipsoid']} (feasible region ellipsoidal)
• Figure 2: A nonconvex $\beta$-fair space. $\Delta(\mathbf{w}):= \mathbf{w}^\top\mathbf{w} - (.3\sqrt{\lvert \mathbf{w}_1\rvert} + .3\sqrt{\lvert \mathbf{w}_2 \rvert} )$ and $\beta = .3$
• Figure 3: Optimal value in various $\beta$-fair equilibria for $\ell_1$ fairness constraints. The desirable features are occupation, workclass, and education.
• Figure 4: Optimal values for varying $\beta$ for different group splits under $\ell_2$-fairness constraint
• Figure 5: Optimal values for varying $\beta$ for different group splits under non-uniform random cost matrices $A_1=2A_2$ and the $\ell_1$-fairness constraint

Theorems & Definitions (83)

• Definition 2.1: Contribution matrix
• Proposition 2.1
• Remark 2.1
• Definition 2.2: $\mathcal{W}(\beta;\Delta)$, the set of $\beta$-fair rules
• Example 3.1: Sum of absolute value differences
• Example 3.2: Sum of squared differences
• Definition 4.1: $\mathcal{F}$, some nonconvex $\beta$-fair spaces
• Example 4.1: Asymmetric desirability fairness
• Lemma A.1: Contribution matrix of a DAG is invertible and kernel zero
• proof : Proof of Lemma \ref{['lem:c_ker_0']}