Sura Alhanouti, Güzin Bayraksan, Parinaz Naghizadehcs.LG cs.GT
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.
A common assumption in strategic classification is that the classifier is public knowledge. However, it remains unclear whether, and why, a system would choose to commit to full disclosure. We study a setting in which regulation requires the system to disclose some, but not all, of the information. This induces a learning task in which the learner must jointly optimize the classifier and the uncertainty surrounding it. To this end, we adopt from robust mechanism design the notion of ambiguity, which in our setting allows the learner to reveal a set or range of possible classifiers, while privately choosing which of them to ultimately realize. We investigate how ambiguity affects the learning task, develop efficient algorithms for computing best-responses and training, and empirically explore strategic learning and its outcomes in this novel setting and using our approach.