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Register a new userStrategic Classification Made Practical
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Added by
Sagi Levanon
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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No Arabic abstract
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.
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The classical Perceptron algorithm provides a simple and elegant procedure for learning a linear classifier. In each step, the algorithm observes the samples position and label and updates the current predictor accordingly if it makes a mistake. However, in presence of strategic agents that desire to be classified as positive and that are able to modify their position by a limited amount, the classifier may not be able to observe the true position of agents but rather a position where the agent pretends to be. Unlike the original setting with perfect knowledge of positions, in this situation the Perceptron algorithm fails to achieve its guarantees, and we illustrate examples with the predictor oscillating between two solutions forever, making an unbounded number of mistakes even though a perfect large-margin linear classifier exists. Our main contribution is providing a modified Perceptron-style algorithm which makes a bounded number of mistakes in presence of strategic agents with both $ell_2$ and weighted $ell_1$ manipulation costs. In our baseline model, knowledge of the manipulation costs (i.e., the extent to which an agent may manipulate) is assumed. In our most general model, we relax this assumption and provide an algorithm which learns and refines both the classifier and its cost estimates to achieve good mistake bounds even when manipulation costs are unknown.
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.
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.
Machine learning techniques can be useful in applications such as credit approval and college admission. However, to be classified more favorably in such contexts, an agent may decide to strategically withhold some of her features, such as bad test scores. This is a missing data problem with a twist: which data is missing {em depends on the chosen classifier}, because the specific classifier is what may create the incentive to withhold certain feature values. We address the problem of training classifiers that are robust to this behavior. We design three classification methods: {sc Mincut}, {sc Hill-Climbing} ({sc HC}) and Incentive-Compatible Logistic Regression ({sc IC-LR}). We show that {sc Mincut} is optimal when the true distribution of data is fully known. However, it can produce complex decision boundaries, and hence be prone to overfitting in some cases. Based on a characterization of truthful classifiers (i.e., those that give no incentive to strategically hide features), we devise a simpler alternative called {sc HC} which consists of a hierarchical ensemble of out-of-the-box classifiers, trained using a specialized hill-climbing procedure which we show to be convergent. For several reasons, {sc Mincut} and {sc HC} are not effective in utilizing a large number of complementarily informative features. To this end, we present {sc IC-LR}, a modification of Logistic Regression that removes the incentive to strategically drop features. We also show that our algorithms perform well in experiments on real-world data sets, and present insights into their relative performance in different settings.
Transmission of disease, spread of information and rumors, adoption of new products, and many other network phenomena can be fruitfully modeled as cascading processes, where actions chosen by nodes influence the subsequent behavior of neighbors in the network graph. Current literature on cascades tends to assume nodes choose myopically based on the state of choices already taken by other nodes. We examine the possibility of strategic choice, where agents representing nodes anticipate the choices of others who have not yet decided, and take into account their own influence on such choices. Our study employs the framework of Chierichetti et al. [2012], who (under assumption of myopic node behavior) investigate the scheduling of node decisions to promote cascades of product adoptions preferred by the scheduler. We show that when nodes behave strategically, outcomes can be extremely different. We exhibit cases where in the strategic setting 100% of agents adopt, but in the myopic setting only an arbitrarily small epsilon % do. Conversely, we present cases where in the strategic setting 0% of agents adopt, but in the myopic setting (100-epsilon)% do, for any constant epsilon > 0. Additionally, we prove some properties of cascade processes with strategic agents, both in general and for particular classes of graphs.
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