Beyond Rational Illusion: Behaviorally Realistic Strategic Classification

Strategic classification studies the problem where self-interested individuals or agents manipulate their response to obtain favorable decision outcomes made by classifiers, typically turning to dishonest actions when they are less costly than genuine efforts. Prior works have demonstrated a fundamental inability to get out of this conundrum by only focusing on the design of a classifier. We note that prior work also heavily focuses on either one-shot settings or repeated interaction with the same classifier. Real-world decision making is often multi-stage, involving a sequence of potentially different classifiers as an agent progresses. This paper introduces a sequential, stochastic, multi-stage model of strategic classification, by capturing how agents adapt their behavior, through improvement actions (enhancing both observable features and true attributes) and gaming actions (enhancing only observable features), over multiple levels of classification with increasing difficulty as well as reward. For each level, we adopt a selective classifier that can abstain from making a prediction at low confidence. Consequently, a positive (resp. negative) outcome leads to promotion (resp. demotion) of the agent to the next higher (resp. lower) level, while abstention keeps the agent at the same level. We fully characterize the agent's optimal instantaneous action under selective classifiers and compare the long-term properties and utility of the agent repeatedly following an optimal myopic policy of either no-improvement (never choose the improvement action) or no-gaming (never choose the gaming action). We further examine design principles over the sequence of classifiers that yield higher long-term utility for the latter policy, thereby effectively incentivizing genuine effort in the long run.

Humans facing algorithmic decision systems have been found to ``game'' them by altering their input data (at a cost to them) in order to favorably change the algorithmic outcomes they receive (at a cost to the algorithm). The growing literature on strategic classification seeks to develop robust machine learning algorithms that account for, and reduce, unwanted strategic behavior. A limitation of these existing works is that they assume the cost of strategic behavior to be fixed and independent of the classifier's decision. In practice, however, manipulation costs evolve and depend on past algorithmic decisions: today's decisions influence tomorrow's costs. This paper proposes and analyzes a two-stage robust optimization framework with a decision-dependent uncertainty set to capture such dependencies. We highlight that awareness of policy-dependent costs not only reduces uncertainty, but also better curtails gaming of the algorithmic system over time.

Algorithmic developments in Strategic Classification have been mostly limited to linear classifiers in settings where the best response has a closed-form solution or can be easily approximated. While some work has explored the role of non-linear classifiers in strategic settings, progress in this direction is impeded by the computational intractability of the strategic behaviour. Addressing this, we present a novel method for approximating the best response by exploiting Lagrangian duality. By reformulating the strategic response as a constrained optimisation problem, we can construct a Lagrangian that is amenable to first order optimisation methods. This approach reproduces closed-form strategic behaviour in linear settings and can be straight-forwardly applied to non-linear settings. We show how the Implicit Function Theorem can be used in conjunction with our proposed response formulation during classifier learning to compute the total gradient of the loss. This connects the classifier parameters directly to the consequent strategic behaviour, yielding a novel training algorithm that can exploit this relationship. Experimental evaluation shows that the resulting models achieve improved strategic accuracy on common machine learning datasets.