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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 may update the current predictor accordingly. In presence of strategic agents, however, the classifier may not be able to observe the true position but a position where the agent pretends to be in order to be classified desirably. 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, never reaching a perfect classifier even though one exists. Our main contribution is providing a modified Perceptron-style algorithm which finds a classifier in presence of strategic agents with both 2 and weighted 1 manipulation costs. In our baseline model, knowledge of the manipulation costs 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.

In this work, we consider classification of agents who can both game and improve. For example, people wishing to get a loan may be able to take some actions that increase their perceived credit-worthiness and others that also increase their true credit-worthiness. A decisionmaker would like to define a classification rule with few false-positives (does not give out many bad loans) while yielding many true positives (giving out many good loans), which includes encouraging agents to improve to become true positives if possible. We consider two models for this problem, a general discrete model and a linear model, and prove algorithmic, learning, and hardness results for each.For the general discrete model, we give an efficient algorithm for the problem of maximizing the number of true positives subject to no false positives, and show how to extend this to a partial-information learning setting. We also show hardness for the problem of maximizing the number of true positives subject to a nonzero bound on the number of false positives, and that this hardness holds even for a finite-point version of our linear model. We also show that maximizing the number of true positives subject to no false positive is NP-hard in our full linear model. We additionally provide an algorithm that determines whether there exists a linear classifier that classifies all agents accurately and causes all improvable agents to become qualified, and give additional results for low-dimensional data.

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Machine Learning (ML) decision-making algorithms are now widely used in predictive decision-making, for example, to determine who to admit and give a loan. Their wide usage and consequential effects on individuals led the ML community to question and raise concerns on how the algorithms differently affect different people and communities. In this paper, we study fairness issues that arise when decision-makers use models (proxy models) that deviate from the models that depict the physical and social environment in which the decisions are situated (intended models). We also highlight the effect of obstacles on individual access and utilization of the models. To this end, we formulate an Equity Framework that considers equal access to the model, equal outcomes from the model, and equal utilization of the model, and consequentially achieves equity and higher social welfare than current fairness notions that aim for equality. We show how the three main aspects of the framework are connected and provide questions to guide decision-makers towards equitable decision-making. We show how failure to consider access, outcome, and utilization would exacerbate proxy gaps leading to an infinite inequity loop that reinforces structural inequities through inaccurate and incomplete ground truth curation. We, therefore, recommend a more critical look at the model design and its effect on equity and a shift towards equity achieving predictive decision-making models.