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Consequential decision-making typically incentivizes individuals to behave strategically, tailoring their behavior to the specifics of the decision rule. A long line of work has therefore sought to counteract strategic behavior by designing more conservative decision boundaries in an effort to increase robustness to the effects of strategic covariate shift. We show that these efforts benefit the institutional decision maker at the expense of the individuals being classified. Introducing a notion of social burden, we prove that any increase in institutional utility necessarily leads to a corresponding increase in social burden. Moreover, we show that the negative externalities of strategic classification can disproportionately harm disadvantaged groups in the population. Our results highlight that strategy-robustness must be weighed against considerations of social welfare and fairness.
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The study of strategic or adversarial manipulation of testing data to fool a classifier has attracted much recent attention. Most previous works have focused on two extreme situations where any testing data point either is completely adversarial or always equally prefers the positive label. In this paper, we generalize both of these through a unified framework for strategic classification, and introduce the notion of strategic VC-dimension (SVC) to capture the PAC-learnability in our general strategic setup. SVC provably generalizes the recent concept of adversarial VC-dimension (AVC) introduced by Cullina et al. arXiv:1806.01471. We instantiate our framework for the fundamental strategic linear classification problem. We fully characterize: (1) the statistical learnability of linear classifiers by pinning down its SVC; (2) its computational tractability by pinning down the complexity of the empirical risk minimization problem. Interestingly, the SVC of linear classifiers is always upper bounded by its standard VC-dimension. This characterization also strictly generalizes the AVC bound for linear classifiers in arXiv:1806.01471.
We design an active learning algorithm for cost-sensitive multiclass classification: problems where different errors have different costs. Our algorithm, COAL, makes predictions by regressing to each labels cost and predicting the smallest. On a new example, it uses a set of regressors that perform well on past data to estimate possible costs for each label. It queries only the labels that could be the best, ignoring the sure losers. We prove COAL can be efficiently implemented for any regression family that admits squared loss optimization; it also enjoys strong guarantees with respect to predictive performance and labeling effort. We empirically compare COAL to passive learning and several active learning baselines, showing significant improvements in labeling effort and test cost on real-world datasets.
Strategic classification regards the problem of learning in settings where users can strategically modify their features to improve outcomes. This setting applies broadly and has received much recent attention. But despite its practical significance, work in this space has so far been predominantly theoretical. In this paper we present a learning framework for strategic classification that is practical. Our approach directly minimizes the strategic empirical risk, achieved by differentiating through the strategic response of users. This provides flexibility that allows us to extend beyond the original problem formulation and towards more realistic learning scenarios. A series of experiments demonstrates the effectiveness of our approach on various learning settings.
We introduce a new class of context dependent, incomplete information games to serve as structured prediction models for settings with significant strategic interactions. Our games map the input context to outcomes by first condensing the input into private player types that specify the utilities, weighted interactions, as well as the initial strategies for the players. The game is played over multiple rounds where players respond to weighted aggregates of their neighbors strategies. The predicted output from the model is a mixed strategy profile (a near-Nash equilibrium) and each observation is thought of as a sample from this strategy profile. We introduce two new aggregator paradigms with provably convergent game dynamics, and characterize the conditions under which our games are identifiable from data. Our games can be parameterized in a transferable manner so that the sets of players can change from one game to another. We demonstrate empirically that our games as models can recover meaningful strategic interactions from real voting data.
This paper studies the statistical complexity of kernel hyperparameter tuning in the setting of active regression under adversarial noise. We consider the problem of finding the best interpolant from a class of kernels with unknown hyperparameters, assuming only that the noise is square-integrable. We provide finite-sample guarantees for the problem, characterizing how increasing the complexity of the kernel class increases the complexity of learning kernel hyperparameters. For common kernel classes (e.g. squared-exponential kernels with unknown lengthscale), our results show that hyperparameter optimization increases sample complexity by just a logarithmic factor, in comparison to the setting where optimal parameters are known in advance. Our result is based on a subsampling guarantee for linear regression under multiple design matrices, combined with an {epsilon}-net argument for discretizing kernel parameterizations.
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