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In this work, we consider classification of agents who can both game andimprove. For example, people wishing to get a loan may be able to take someactions that increase their perceived credit-worthiness and others that alsoincrease their true credit-worthiness. A decision-maker would like to define aclassification rule with few false-positives (does not give out many bad loans)while yielding many true positives (giving out many good loans), which includesencouraging agents to improve to become true positives if possible. We considertwo models for this problem, a general discrete model and a linear model, andprove algorithmic, learning, and hardness results for each. For the generaldiscrete model, we give an efficient algorithm for the problem of maximizingthe number of true positives subject to no false positives, and show how toextend this to a partial-information learning setting. We also show hardnessfor the problem of maximizing the number of true positives subject to a nonzerobound on the number of false positives, and that this hardness holds even for afinite-point version of our linear model. We also show that maximizing thenumber of true positives subject to no false positive is NP-hard in our fulllinear model. We additionally provide an algorithm that determines whetherthere exists a linear classifier that classifies all agents accurately andcauses all improvable agents to become qualified, and give additional resultsfor low-dimensional data.

On classification of strategic agents who can both game and improve