Estimation of Utility-Maximizing Bounds on Potential Outcomes
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Estimation of individual treatment effects is often used as the basis for contextual decision making in fields such as healthcare, education, and economics. However, in many real-world applications it is sufficient for the decision maker to have upper and lower bounds on the potential outcomes of decision alternatives, allowing them to evaluate the trade-off between benefit and risk. With this in mind, we develop an algorithm for directly learning upper and lower bounds on the potential outcomes under treatment and non-treatment. Our theoretical analysis highlights a trade-off between the complexity of the learning task and the confidence with which the resulting bounds cover the true potential outcomes; the more confident we wish to be, the more complex the learning task is. We suggest a novel algorithm that maximizes a utility function while maintaining valid potential outcome bounds. We illustrate different properties of our algorithm, and highlight how it can be used to guide decision making using two semi-simulated datasets.
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